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    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerDivides",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerQuotPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerQuotPrefix",
      "target": "DivRem"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerQuotPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerQuotPrefix",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Prime",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentPrefixGCD",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentPrefixGCD",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentPrefixGCD",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeFactorToggle",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Product",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Product",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "QRes",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Range",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Range",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RationalApproximationError",
      "target": "NaturalAbsDifference"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Repeat",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Repeat",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RoundedSignedDivision",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RoundedSignedDivision",
      "target": "SignedDifferenceSquare"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAdd",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingCofactorTerm",
      "target": "Even"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingCofactorTerm",
      "target": "Odd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedBalance",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedBestApproximationSecondKind",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedBestApproximationSecondKind",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedBestApproximationSecondKind",
      "target": "NaturalAbsDifference"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedBezout",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDerivativeNonzero",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDerivativeUnit",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDerivativeUnit",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantNodeAt",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantNodeAt",
      "target": "SignedDeterminantNodeCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedFloor",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMatrixPrefixEquality",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMatrixPrefixEquality",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMul",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedNegate",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSelectedSubmatrix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSelectedSubmatrix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SmallerFermatFourCounterexample",
      "target": "FermatFourCounterexample"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SmallerFermatFourCounterexample",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Sorted",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Sorted",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Sorted",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SuccessorInverse",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SurjectivePrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SurjectivePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UniformBetaPrefixBox",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UniformBetaPrefixBox",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Unit",
      "target": "Mod"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitResidue",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "WeakMW",
      "target": "SelmerWitness"
    },
    {
      "kind": "definition_uses_definition",
      "source": "WeightedSignedNormThree",
      "target": "SignedDifferenceSquare"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ZPairDecode",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AllPrime",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AllPrime",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AllPrime",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AllRootLifts",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAt",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAt",
      "target": "MatrixMinorFourCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAt",
      "target": "SignedBalance"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithTable",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithTable",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithTable",
      "target": "MatrixMinorFourCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithTable",
      "target": "SignedBalance"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BertrandWindow",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BertrandWindow",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExponentDigitCode",
      "target": "BinaryDigitPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExponentDigitCode",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryModularPower",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryModularPower",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryModularStep",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BitCount",
      "target": "AllBits"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BitLen",
      "target": "PowTwo"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BoundedNonzeroInverse",
      "target": "BalancedInverse"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BoundedNonzeroInverse",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BoundedPowerValuation",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BoundedPowerValuation",
      "target": "PowerDivides"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTCanonicalPrefixSolution",
      "target": "CRTPrefixLCM"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTCanonicalPrefixSolution",
      "target": "CRTPrefixSolution"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTCanonicalPrefixSolution",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTMergeCompatiblePrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTMergeCompatiblePrefix",
      "target": "CRTPrefixLCM"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTMergeCompatiblePrefix",
      "target": "CRTPrefixSolution"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTMergeCompatiblePrefix",
      "target": "Gcd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTMergeCompatiblePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTMergeCompatiblePrefix",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTNormalizedPrefixSolution",
      "target": "CRTPrefixLCM"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTNormalizedPrefixSolution",
      "target": "CRTPrefixSolution"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTNormalizedPrefixSolution",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCompatiblePrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCompatiblePrefix",
      "target": "Gcd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCompatiblePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCompatiblePrefix",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPrefixGcdCongruences",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPrefixGcdCongruences",
      "target": "IsGCD"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPrefixGcdCongruences",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPrefixGcdCongruences",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CentralBinom",
      "target": "Choose"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConvergentMatrixAt",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConvergentMatrixAt",
      "target": "ConvergentMatrixCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Coprime",
      "target": "Gcd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaRoot",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaRoot",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaRoot",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaTransitionAt",
      "target": "CornacchiaStateAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaTransitionAt",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorComplementPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorComplementPrefix",
      "target": "DivisorComplement"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorComplementPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorPrimeToggle",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorPrimeToggle",
      "target": "PrimeFactorToggle"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ECCount",
      "target": "Curve"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ECCount",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanAnchoredExecution",
      "target": "ContinuedFractionTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanAnchoredExecution",
      "target": "EuclideanStateAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanAnchoredExecution",
      "target": "Gcd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanBoundedTrace",
      "target": "ContinuedFractionTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanBoundedTrace",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanExecution",
      "target": "ContinuedFractionTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanExecution",
      "target": "Gcd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerPrimePowerFactor",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerPrimePowerFactor",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Eval",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Factorial",
      "target": "Product"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Factorial",
      "target": "Range"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Factorization",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FermatFourStrictDescent",
      "target": "FermatFourCounterexample"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FermatFourStrictDescent",
      "target": "SmallerFermatFourCounterexample"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FiniteField",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpAdd",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpAdd",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCardinality",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCardinality",
      "target": "IdentityMatrixSelector"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCardinality",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientReduction",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientReduction",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientReduction",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpElement",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpElement",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMonic",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMonic",
      "target": "BetaPrefixInto"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMul",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMul",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolynomialTrim",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolynomialTrim",
      "target": "BetaPrefixInto"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolynomialTrim",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolynomialTrim",
      "target": "PolynomialSuffix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpRepresentedDegree",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpRepresentedDegree",
      "target": "BetaPrefixInto"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GaussBit",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GaussianSignedDivisionRemainder",
      "target": "GaussianSignedNorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GaussianSignedDivisionRemainder",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HasPrimeSquareDivisor",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HasPrimeSquareDivisor",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerDerivative",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerDerivative",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerDerivative",
      "target": "HornerDerivativeTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerRootModulo",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerRootModulo",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "IntegerMatrixEntrywiseEqual",
      "target": "IntegerVectorEqual"
    },
    {
      "kind": "definition_uses_definition",
      "source": "IntegerVectorNegate",
      "target": "IntegerVectorEqual"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InverseIndex",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InverseIndex",
      "target": "SuccessorInverse"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Irred",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixMinorCell",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixMinorCell",
      "target": "MatrixSkipIndex"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixProductCell",
      "target": "DotProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixProductCell",
      "target": "MatrixAffineSlice"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularDysonTransform",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularDysonTransform",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularDysonTransform",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularDysonTransform",
      "target": "ModularSetMember"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularSetSum",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularSetSum",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularSetSum",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularSetSum",
      "target": "ModularSetMember"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularTranslationBoundary",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularTranslationBoundary",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularTranslationBoundary",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ModularTranslationBoundary",
      "target": "ModularSetMember"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultinomialBinomialPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultinomialBinomialPrefix",
      "target": "Choose"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultinomialBinomialPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NextPrime",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NextPrime",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NextPrime",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PermutationPrefix",
      "target": "BoundedPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PermutationPrefix",
      "target": "InjectivePrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PermutationPrefix",
      "target": "SurjectivePrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PolynomialDiagonalTerm",
      "target": "BetaZeroExtend"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeBitPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeBitPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeBitPrefix",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeDivisorSupport",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeDivisorSupport",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeDivisorSupport",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeDivisorSupport",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeThreeModFourDivisor",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeThreeModFourDivisor",
      "target": "Mod4Three"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeThreeModFourDivisor",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitiveRootModulus",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Primorial",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Primorial",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Primorial",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Primorial",
      "target": "Product"
    },
    {
      "kind": "definition_uses_definition",
      "source": "QuadBit",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "QuadBit",
      "target": "Mod"
    },
    {
      "kind": "definition_uses_definition",
      "source": "QuadBit",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledFixedPoint",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledFixedPoint",
      "target": "UnitResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInverse",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInverse",
      "target": "UnitResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingProductPrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingProductPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingProductPrefix",
      "target": "SignedAlternatingCofactorTerm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCodeFloor",
      "target": "SignedDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCodeFloor",
      "target": "SignedFloor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDotProduct",
      "target": "DotProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedHornerRoot",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedHornerRoot",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedPrefixSum",
      "target": "BetaSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedPrefixSum",
      "target": "MatrixMinorFourCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedPrefixSum",
      "target": "SignedBalance"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SimpleLift",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Squarefree",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Squarefree",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Squarefree",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "TeichLift",
      "target": "Mod"
    },
    {
      "kind": "definition_uses_definition",
      "source": "TeichLift",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitMultiplierPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitMultiplierPrefix",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitMultiplierPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Val",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Val",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "WeierstrassCertificate",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ZPairRep",
      "target": "SignedBalance"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ZPairValid",
      "target": "ZPairDecode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAdd",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAdd",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAdd",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithAdd",
      "target": "SignedAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithMul",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithMul",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithMul",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithMul",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithNegate",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithNegate",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithNegate",
      "target": "SignedNegate"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithPositiveEqual",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithPositiveEqual",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithReindex",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithReindex",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithReindex",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithScale",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithScale",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithScale",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithScale",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithSlice",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithSlice",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithSlice",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithTableEqual",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithTableEqual",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BertrandChain",
      "target": "BertrandWindow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BertrandChain",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BertrandChain",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BetaValuationPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BetaValuationPrefix",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BetaValuationPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryCanonicalExponentDigitCode",
      "target": "BinaryExponentDigitCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryCanonicalExponentDigitCode",
      "target": "BitLen"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryColumnCarryCount",
      "target": "BinaryAddCarryPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryColumnCarryCount",
      "target": "BitCount"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryColumnCarryCount",
      "target": "PowerQuotPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExecutionOperationCount",
      "target": "BitCount"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExecutionPowerInvariant",
      "target": "BinaryModularPower"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExecutionPowerInvariant",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExecutionTrace",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExecutionTrace",
      "target": "BinaryModularStep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryExecutionTrace",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCoprimePrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCoprimePrefix",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CRTPairwiseCoprimePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CanonicalHornerLift",
      "target": "HornerRootModulo"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CanonicalHornerLift",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CanonicalHornerLift",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CanonicalSignedHornerLift",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CanonicalSignedHornerLift",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CanonicalSignedHornerLift",
      "target": "SignedHornerRoot"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConstantOneTable",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConstantOneTable",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConstantOneTable",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConvergentMatrixTrace",
      "target": "ConvergentMatrixAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConvergentMatrixTrace",
      "target": "ListCell"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ConvergentMatrixTrace",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaEuclideanRun",
      "target": "CornacchiaStateAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaEuclideanRun",
      "target": "CornacchiaTransitionAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaEuclideanRun",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaStateInvariant",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaStateInvariant",
      "target": "CornacchiaAlternatingCongruences"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaStateInvariant",
      "target": "CornacchiaRoot"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaStateInvariant",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletEntry",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletEntry",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletEntry",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGridEntry",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGridEntry",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGridEntry",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletUnitAtOne",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorMaskEntry",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorMaskEntry",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorPrimeTogglePrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorPrimeTogglePrefix",
      "target": "DivisorPrimeToggle"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorPrimeTogglePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EMul",
      "target": "ZPairRep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ENorm",
      "target": "EisensteinCoordinateNorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ENorm",
      "target": "ZPairRep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclidParameters",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclidParameters",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclidParameters",
      "target": "OppositeParity"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclidParametrization",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclidParametrization",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclidParametrization",
      "target": "OppositeParity"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanLogarithmicExecution",
      "target": "BitLen"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanLogarithmicExecution",
      "target": "EuclideanAnchoredExecution"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EuclideanLogarithmicExecution",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerFactorPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerFactorPrefix",
      "target": "EulerPrimePowerFactor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerFactorPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpAddGridValue",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientNegation",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientNegation",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientNegation",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientSubtraction",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientSubtraction",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCoefficientSubtraction",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerStep",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerStep",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerStep",
      "target": "FpMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpInv",
      "target": "FpMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMulGridValue",
      "target": "FpMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpNeg",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpNegPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpNegPrefix",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpNegPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyAdd",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyAdd",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyAdd",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyScale",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyScale",
      "target": "FpMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyScale",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpUnitSteps",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpUnitSteps",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpUnitSteps",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GMul",
      "target": "ZPairRep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GNorm",
      "target": "GaussianSignedNorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GNorm",
      "target": "ZPairRep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerDerivativeOnly",
      "target": "HornerDerivative"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerTaylorRemainder",
      "target": "Horner"
    },
    {
      "kind": "definition_uses_definition",
      "source": "HornerTaylorRemainder",
      "target": "HornerDerivative"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InitialPrimeChain",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InitialPrimeChain",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InitialPrimeChain",
      "target": "NextPrime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InversePrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InversePrefix",
      "target": "InverseIndex"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InversePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "JacobiBit",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "KroneckerDeltaTable",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "KroneckerDeltaTable",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "KroneckerDeltaTable",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "LiftedPowerDifference",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "LiftedPowerDifference",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "LiftedPowerDifference",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixMinorPrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixMinorPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixMinorPrefix",
      "target": "MatrixMinorCell"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixProductPrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixProductPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MatrixProductPrefix",
      "target": "MatrixProductCell"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusPositiveValues",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusPositiveValues",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusPositiveValues",
      "target": "Mobius"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusTable",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusTable",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusTable",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MobiusTable",
      "target": "Mobius"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Multinomial",
      "target": "BetaSumTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Multinomial",
      "target": "MultinomialBinomialPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Multinomial",
      "target": "Product"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultiplicativePrefix",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultiplicativePrefix",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultiplicativePrefix",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultiplicativePrefix",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultiplicativePrefix",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NaturalSquarefreeDecomposition",
      "target": "Squarefree"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PolynomialDiagonalPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PolynomialDiagonalPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PolynomialDiagonalPrefix",
      "target": "PolynomialDiagonalTerm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerValuation",
      "target": "Val"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentEntries",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentEntries",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentEntries",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentEntries",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeExponentEntries",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeFactorList",
      "target": "AllPrime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeFactorList",
      "target": "Product"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeFactorListPermutation",
      "target": "FactorListMatching"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeFactorListPermutation",
      "target": "PermutationPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimePowerValuation",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimePowerValuation",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationsDivisible",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationsDivisible",
      "target": "Dvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationsDivisible",
      "target": "Prime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitiveFermatFourCounterexample",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitiveFermatFourCounterexample",
      "target": "FermatFourCounterexample"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitivePythagorean",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitivePythagorean",
      "target": "Pythagorean"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInverseIndex",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInverseIndex",
      "target": "ScaledInverse"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingCofactorFold",
      "target": "BetaSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedAlternatingCofactorFold",
      "target": "SignedAlternatingProductPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCartesianProduct",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCartesianProduct",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCartesianProduct",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCartesianProduct",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedHornerValueDerivative",
      "target": "HornerDerivative"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceEntry",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceEntry",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportReindex",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportReindex",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportReindex",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportReindex",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedZeroWindow",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedZeroWindow",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedZeroWindow",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SimpleHornerRoot",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SimpleHornerRoot",
      "target": "HornerDerivative"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SimpleHornerRoot",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitBitPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitBitPrefix",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitBitPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitProductFactor",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitScaledPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitScaledPrefix",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitScaledPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitScaledPrefix",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ZPairAdd",
      "target": "ZPairRep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithExtend",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithExtend",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithExtend",
      "target": "ArithTableEqual"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryModularExecution",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryModularExecution",
      "target": "BinaryExecutionTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Convergent",
      "target": "ConvergentMatrixTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaTrace",
      "target": "CornacchiaEuclideanRun"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CornacchiaTrace",
      "target": "CornacchiaRoot"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletDivisorGridWitness",
      "target": "DirichletEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletDivisorGridWitness",
      "target": "DivisorFactorPair"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletDivisorGridWitness",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletDivisorGridWitness",
      "target": "SignedMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFactorRow",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFactorRow",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFactorRow",
      "target": "DirichletGridEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFactorRow",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFlatEntry",
      "target": "DirichletGridEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFlatEntry",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGrid",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGrid",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGrid",
      "target": "DirichletGridEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletGrid",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletPrefix",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletPrefix",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletPrefix",
      "target": "DirichletEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletPrefix",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorMask",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorMask",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorMask",
      "target": "DivisorMaskEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorMask",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EDivRem",
      "target": "EMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EDivRem",
      "target": "ZPairAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FactorParitySign",
      "target": "AlternatingSignedUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FactorParitySign",
      "target": "PrimeFactorList"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FactorialValuation",
      "target": "Fact"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FactorialValuation",
      "target": "PowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpAddPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpAddPrefix",
      "target": "FpAddGridValue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpAddPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpConvolutionCoefficient",
      "target": "BetaSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpConvolutionCoefficient",
      "target": "CanonicalModularResidue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpConvolutionCoefficient",
      "target": "PolynomialDiagonalPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFieldLaws",
      "target": "FpAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFieldLaws",
      "target": "FpInv"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFieldLaws",
      "target": "FpMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFieldLaws",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerSteps",
      "target": "FpHornerStep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerSteps",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMonicNormalization",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMonicNormalization",
      "target": "FpInv"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMonicNormalization",
      "target": "FpPolyScale"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMulPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMulPrefix",
      "target": "FpMulGridValue"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpMulPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpUnitTrace",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpUnitTrace",
      "target": "FpUnitSteps"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpZeroExtendedInv",
      "target": "FpInv"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpZeroExtendedInv",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GBezout",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GBezout",
      "target": "ZPairAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GDivRem",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GDivRem",
      "target": "ZPairAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GDvd",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProductStep",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProductStep",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "InitialPrimeList",
      "target": "InitialPrimeChain"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultinomialCarryPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultinomialCarryPrefix",
      "target": "BinaryColumnCarryCount"
    },
    {
      "kind": "definition_uses_definition",
      "source": "MultinomialCarryPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerValuationOne",
      "target": "PowerValuation"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationSupport",
      "target": "InjectivePrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationSupport",
      "target": "PrimeDivisorSupport"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationSupport",
      "target": "PrimeExponentEntries"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimeValuationSupport",
      "target": "Product"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitiveTriple",
      "target": "PrimitivePythagorean"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInversePrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInversePrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ScaledInversePrefix",
      "target": "ScaledInverseIndex"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedFirstRowCofactorFold",
      "target": "MatrixAffineSlice"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedFirstRowCofactorFold",
      "target": "SignedAlternatingCofactorFold"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceFlatEntry",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceFlatEntry",
      "target": "SignedIncidenceEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMatrixMinor",
      "target": "MatrixMinorPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMatrixProduct",
      "target": "MatrixPointwiseAdd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMatrixProduct",
      "target": "MatrixProductPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedNonsingularHornerRoot",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedNonsingularHornerRoot",
      "target": "SignedDerivativeNonzero"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedNonsingularHornerRoot",
      "target": "SignedHornerValueDerivative"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSimpleHornerRoot",
      "target": "ModEq"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSimpleHornerRoot",
      "target": "SignedDerivativeUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSimpleHornerRoot",
      "target": "SignedHornerValueDerivative"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSliceSum",
      "target": "ArithSlice"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSliceSum",
      "target": "SignedPrefixSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportIncidence",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportIncidence",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportIncidence",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSupportIncidence",
      "target": "SignedIncidenceEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedWeightedSum",
      "target": "ArithMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedWeightedSum",
      "target": "SignedPrefixSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitCount",
      "target": "BetaSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitCount",
      "target": "UnitBitPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitProductPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitProductPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "UnitProductPrefix",
      "target": "UnitProductFactor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithRowSums",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithRowSums",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithRowSums",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "ArithRowSums",
      "target": "SignedSliceSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryCompleteModularExecution",
      "target": "BinaryCanonicalExponentDigitCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryCompleteModularExecution",
      "target": "BinaryModularExecution"
    },
    {
      "kind": "definition_uses_definition",
      "source": "BinaryCompleteModularExecution",
      "target": "BinaryModularPower"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CarryCountMany",
      "target": "BetaSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CarryCountMany",
      "target": "BetaSumTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "CarryCountMany",
      "target": "MultinomialCarryPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletCoprimeProductData",
      "target": "Coprime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletCoprimeProductData",
      "target": "DirichletPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletCoprimeProductData",
      "target": "DivisorPairIndexMap"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletCoprimeProductData",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletCoprimeProductData",
      "target": "MultiplicativePrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletCoprimeProductData",
      "target": "SignedCartesianProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFlatPrefix",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFlatPrefix",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFlatPrefix",
      "target": "DirichletFlatEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletFlatPrefix",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletSum",
      "target": "DirichletPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletSum",
      "target": "SignedPrefixSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorSum",
      "target": "DivisorMask"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorSum",
      "target": "SignedPrefixSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EEuclideanDivision",
      "target": "EDivRem"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EEuclideanDivision",
      "target": "ENorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EEuclideanDivision",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerProduct",
      "target": "EulerFactorPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerProduct",
      "target": "PrimeValuationSupport"
    },
    {
      "kind": "definition_uses_definition",
      "source": "EulerProduct",
      "target": "Product"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpConvolutionPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpConvolutionPrefix",
      "target": "FpConvolutionCoefficient"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpConvolutionPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerTrace",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerTrace",
      "target": "FpHornerSteps"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHornerTrace",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpInvPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpInvPrefix",
      "target": "FpZeroExtendedInv"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpInvPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpUnitMultiple",
      "target": "FpUnitTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GEuclideanDivision",
      "target": "GDivRem"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GEuclideanDivision",
      "target": "GNorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GEuclideanDivision",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GEuclideanDivision",
      "target": "ZPairValid"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GGcd",
      "target": "GDvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProductSteps",
      "target": "GProductStep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProductSteps",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GUnit",
      "target": "GDvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "IntegerMatrixVectorProduct",
      "target": "IntegerVectorEqual"
    },
    {
      "kind": "definition_uses_definition",
      "source": "IntegerMatrixVectorProduct",
      "target": "SignedMatrixProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PerfectPowerProfileData",
      "target": "PerfectPowerProfileCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PerfectPowerProfileData",
      "target": "PerfectPowerRootTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PerfectPowerProfileData",
      "target": "PrimeExponentPrefixGCD"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PerfectPowerProfileData",
      "target": "PrimeValuationSupport"
    },
    {
      "kind": "definition_uses_definition",
      "source": "Phi",
      "target": "UnitCount"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantChildPrefix",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantChildPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantChildPrefix",
      "target": "SignedDeterminantNodeAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantChildPrefix",
      "target": "SignedMatrixMinor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceFlatPrefix",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceFlatPrefix",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceFlatPrefix",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedIncidenceFlatPrefix",
      "target": "SignedIncidenceFlatEntry"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMinorRecord",
      "target": "MatrixMinorFourCode"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedMinorRecord",
      "target": "SignedMatrixMinor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletTable",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletTable",
      "target": "ArithTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletTable",
      "target": "DirichletSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletTable",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorTransform",
      "target": "ArithAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorTransform",
      "target": "DivisorSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DivisorTransform",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCharacteristic",
      "target": "FpUnitMultiple"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpCharacteristic",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpHorner",
      "target": "FpHornerTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpOperationTables",
      "target": "FpAddPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpOperationTables",
      "target": "FpInvPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpOperationTables",
      "target": "FpMulPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpOperationTables",
      "target": "FpNegPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyProduct",
      "target": "BetaPrefixInto"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyProduct",
      "target": "FpConvolutionPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpPolyProduct",
      "target": "PolynomialProductLength"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpSyntheticDivision",
      "target": "FpHornerTrace"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpSyntheticDivision",
      "target": "MatrixAffineSlice"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAssociate",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAssociate",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducible",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducible",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducible",
      "target": "ZPairValid"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrime",
      "target": "GDvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrime",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrime",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrime",
      "target": "ZPairValid"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProduct",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProduct",
      "target": "GProductSteps"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProperNormDivisor",
      "target": "GDvd"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProperNormDivisor",
      "target": "GNorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProperNormDivisor",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GProperNormDivisor",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GStrictNonunitFactorization",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GStrictNonunitFactorization",
      "target": "GNorm"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GStrictNonunitFactorization",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GStrictNonunitFactorization",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "IntegerColumnSpan",
      "target": "IntegerMatrixVectorProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerProfile",
      "target": "PerfectPowerProfileData"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PowerProfile",
      "target": "Pow"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitiveRoot",
      "target": "Order"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PrimitiveRoot",
      "target": "Phi"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCofactorMinorPrefix",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCofactorMinorPrefix",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedCofactorMinorPrefix",
      "target": "SignedMinorRecord"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantLocalStep",
      "target": "SignedAlternatingCofactorFold"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantLocalStep",
      "target": "SignedDeterminantChildPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedRectangularSum",
      "target": "ArithRowSums"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedRectangularSum",
      "target": "SignedPrefixSum"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletInverse",
      "target": "DirichletTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "DirichletInverse",
      "target": "KroneckerDeltaTable"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFiniteStructure",
      "target": "FpCardinality"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFiniteStructure",
      "target": "FpCharacteristic"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFiniteStructure",
      "target": "FpFieldLaws"
    },
    {
      "kind": "definition_uses_definition",
      "source": "FpFiniteStructure",
      "target": "FpOperationTables"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAllIrreducible",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAllIrreducible",
      "target": "GIrreducible"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAllIrreducible",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAllPrime",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAllPrime",
      "target": "GPrime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GAllPrime",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GFactorAssociateMatching",
      "target": "BetaAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GFactorAssociateMatching",
      "target": "GAssociate"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GFactorAssociateMatching",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantHistory",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantHistory",
      "target": "SignedDeterminantLocalStep"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedDeterminantHistory",
      "target": "SignedDeterminantNodeAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducibleFactorization",
      "target": "GAllIrreducible"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducibleFactorization",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducibleFactorization",
      "target": "GProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GIrreducibleFactorization",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GMatchedFactors",
      "target": "GFactorAssociateMatching"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GMatchedFactors",
      "target": "PermutationPrefix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrimeFactorization",
      "target": "GAllPrime"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrimeFactorization",
      "target": "GMul"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrimeFactorization",
      "target": "GProduct"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GPrimeFactorization",
      "target": "GUnit"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedRecursiveDeterminant",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedRecursiveDeterminant",
      "target": "SignedDeterminantHistory"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedRecursiveDeterminant",
      "target": "SignedDeterminantNodeAt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AbsoluteRecursiveDeterminant",
      "target": "SignedRecursiveDeterminant"
    },
    {
      "kind": "definition_uses_definition",
      "source": "GFactorPermutation",
      "target": "GMatchedFactors"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedEvaluatedCofactors",
      "target": "Beta"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedEvaluatedCofactors",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedEvaluatedCofactors",
      "target": "SignedMatrixMinor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedEvaluatedCofactors",
      "target": "SignedRecursiveDeterminant"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSelectedDeterminant",
      "target": "SignedRecursiveDeterminant"
    },
    {
      "kind": "definition_uses_definition",
      "source": "SignedSelectedDeterminant",
      "target": "SignedSelectedSubmatrix"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AllSignedMinorsZero",
      "target": "FiniteMatrixSelector"
    },
    {
      "kind": "definition_uses_definition",
      "source": "AllSignedMinorsZero",
      "target": "SignedSelectedDeterminant"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NonzeroSelectedMinor",
      "target": "FiniteMatrixSelector"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NonzeroSelectedMinor",
      "target": "SignedSelectedDeterminant"
    },
    {
      "kind": "definition_uses_definition",
      "source": "PositiveDeterminantMatrixData",
      "target": "AbsoluteRecursiveDeterminant"
    },
    {
      "kind": "definition_uses_definition",
      "source": "NonzeroMatrixMinor",
      "target": "NonzeroSelectedMinor"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RectangularMatrixRank",
      "target": "AllSignedMinorsZero"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RectangularMatrixRank",
      "target": "Le"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RectangularMatrixRank",
      "target": "Lt"
    },
    {
      "kind": "definition_uses_definition",
      "source": "RectangularMatrixRank",
      "target": "NonzeroMatrixMinor"
    }
  ],
  "definition_page_overrides": {
    "ND0251": {
      "name": "ArithTable",
      "proof_authority": false,
      "registry_route": "signed-arithmetic",
      "route": "dirichlet-convolution"
    },
    "ND0252": {
      "name": "ArithAt",
      "proof_authority": false,
      "registry_route": "signed-arithmetic",
      "route": "dirichlet-convolution"
    },
    "ND0253": {
      "name": "SignedPrefixSum",
      "proof_authority": false,
      "registry_route": "signed-arithmetic",
      "route": "dirichlet-convolution"
    },
    "ND0254": {
      "name": "ArithTableEqual",
      "proof_authority": false,
      "registry_route": "signed-arithmetic",
      "route": "dirichlet-convolution"
    },
    "ND0261": {
      "name": "ArithReindex",
      "proof_authority": false,
      "registry_route": "signed-arithmetic",
      "route": "dirichlet-convolution"
    },
    "ND0262": {
      "name": "BetaPrefixInto",
      "proof_authority": false,
      "registry_route": "finite-prefix-data",
      "route": "prime-field-polynomials"
    },
    "ND0263": {
      "name": "BetaPrefixEqual",
      "proof_authority": false,
      "registry_route": "finite-prefix-data",
      "route": "prime-field-polynomials"
    },
    "PD0047": {
      "name": "PrimePowerValuation",
      "proof_authority": false,
      "registry_route": "bertrand-postulate",
      "route": "multinomial-kummer"
    }
  },
  "definitions": [
    {
      "arity": 8,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [],
      "dependents": [
        "ConvergentErrorInvariant"
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      "expansion": "u · V + 1 = U · v ∧ (a · v = b · u + E ∧ b · U = a · V + F) ∨ U · v + 1 = u · V ∧ (b · u = a · v + E ∧ a · V = b · U + F)",
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      "meaning": "Exactly both zero-coordinate orientations in the complete natural Fermat-four classification.",
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      "expansion": "∀i x. Lt(i,l) ∧ Beta(b,c,i,x) → (x=0 ∨ x=1)",
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      "expansion": "∀ pc_index_secondwave. Lt(pc_index_secondwave,l) → ∃ x. BetaAt(d,f,pc_index_secondwave,x) ∧ (Lt(pc_index_secondwave,u) ∧ x = 0 ∨ Le(u,pc_index_secondwave) ∧ BetaAt(b,c,pc_index_secondwave,x))",
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      "expansion": "∀ mdr_i_pfp_lowertier. ∀ mdr_a_pfp_lowertier. Lt(mdr_i_pfp_lowertier,l) → BetaAt(b,c,mdr_i_pfp_lowertier,mdr_a_pfp_lowertier) → BetaAt(d,e,mdr_i_pfp_lowertier,mdr_a_pfp_lowertier)",
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      "expansion": "∀ fom_index_pfp_lowertier. Lt(fom_index_pfp_lowertier,l) → ∃ x. BetaAt(b,c,fom_index_pfp_lowertier,x) ∧ Lt(x,B)",
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      "expansion": "∃u v. Beta(u,v,0,0) ∧ Beta(u,v,l,z) ∧ ∀i. Lt(i,l) → ∃a x y. Beta(b,c,i,a) ∧ Beta(u,v,i,x) ∧ Beta(u,v,S(i),y) ∧ y=x+a",
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      "expansion": "BetaAt(sb,sc,0,0) ∧ (BetaAt(sb,sc,l,n) ∧ (∀ x. Lt(x,l) → ∃ y. ∃ z. ∃ m. BetaAt(b,c,x,y) ∧ (BetaAt(sb,sc,x,z) ∧ (BetaAt(sb,sc,S x,m) ∧ m = z + y))))",
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      "name": "BinaryAddCarryPrefix",
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      "expansion": "∃u v k q. Beta(k,q,0,0) ∧ Beta(k,q,ell,z) ∧ ∀i. Lt(i,ell) → ∃a s t r w. Beta(b,c,i,a) ∧ Beta(d,e,i,s) ∧ Beta(u,v,i,t) ∧ t=a*s ∧ Beta(k,q,i,r) ∧ Beta(k,q,i+1,w) ∧ w=r+t",
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        "reviewed_id": "ND0158",
        "reviewed_name": "GaussianSignedNorm",
        "reviewed_parameters": [
          "ap",
          "an",
          "bp",
          "bn",
          "N"
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        "route": "gaussian-integers"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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        "GNorm",
        "GProperNormDivisor",
        "GStrictNonunitFactorization",
        "GaussianSignedDivisionRemainder"
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    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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        "EuclideanAnchoredExecution",
        "EuclideanExecution"
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      "expansion": "Dvd(g,a) ∧ Dvd(g,b) ∧ ∀ d. Dvd(d,a) ∧ Dvd(d,b) → Dvd(d,g)",
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      "meaning": "Canonical greatest common divisor.",
      "milestone_users": [
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        "G012",
        "G019",
        "G101"
      ],
      "name": "Gcd",
      "parameters": [
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "reviewed_id": "PD0006",
        "reviewed_name": "IsGCD",
        "reviewed_parameters": [
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        "route": "quadratic-reciprocity"
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      "topological_layer": 1,
      "transitive_dependencies": [
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      "transitive_dependents": [
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        "DirichletCoprimeProductData",
        "EuclidParameters",
        "EuclidParametrization",
        "EuclideanAnchoredExecution",
        "EuclideanExecution",
        "EuclideanLogarithmicExecution",
        "JacobiBit",
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        "PrimitiveFermatFourCounterexample",
        "PrimitivePythagorean",
        "PrimitiveRoot",
        "PrimitiveTriple",
        "SimpleHornerRoot",
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        "UnitCount",
        "UnitProductFactor",
        "UnitProductPrefix",
        "UnitScaledPrefix"
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    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "Lt(t,p) ∧ ModEq(p,q+d*t,0)",
      "expansion_sha256": "1519a6ac3b7c6e84aa74a5b404b04a16f0479755bfb4976c35d310ffbf3f6444",
      "meaning": "A canonical bounded correction digit making the derivative-weighted residual vanish modulo its actual modulus.",
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      "name": "HenselCorrection",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "reviewed_name": "HenselCorrection",
        "reviewed_parameters": [
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        "route": "polynomial-taylor-hensel"
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      "transitive_dependencies": [
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    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "HilbertBit"
      ],
      "dependents": [],
      "expansion": "w is the canonical DUPLICATE-FREE list containing EXACTLY ONCE the real place, the dyadic prime 2, and EVERY prime dividing any numerator or denominator of nonzero rationals a,b; for EACH listed place v it also supplies and verifies the actual local value HilbertBit(a,b,v,s_v)",
      "expansion_sha256": "ab92667685985880894ed943d46185992ce202ef18470a53f4366f163e8f46d7",
      "meaning": "Complete canonical verified finite rational Hilbert support.",
      "milestone_users": [
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      "name": "HilbertProduct",
      "parameters": [
        "a",
        "b",
        "w"
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      "reviewed_incompatibility": null,
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    {
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      "dependencies": [
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      "dependents": [
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        "BinaryExponentDigitCode",
        "Eval",
        "HornerDerivative",
        "HornerRootModulo",
        "HornerTaylorRemainder",
        "SignedHornerRoot"
      ],
      "expansion": "∃u v. Beta(u,v,0,0) ∧ Beta(u,v,ell,z) ∧ ∀i. Lt(i,ell) → ∃a r s. Beta(b,c,i,a) ∧ Beta(u,v,i,r) ∧ Beta(u,v,i+1,s) ∧ s=r*x+a",
      "expansion_sha256": "941a7b111328aef72d1aaf87e2098cff1b41e716583ef849636681b13ad22d3b",
      "meaning": "An exact beta-coded natural-polynomial evaluation trace.",
      "milestone_users": [
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      "name": "Horner",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "blueprint_name": "Horner",
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        "reviewed_name": "Horner",
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        "route": "polynomial-horner"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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        "BinaryExponentDigitCode",
        "CanonicalHornerLift",
        "CanonicalSignedHornerLift",
        "Eval",
        "HornerDerivative",
        "HornerDerivativeOnly",
        "HornerRootModulo",
        "HornerTaylorRemainder",
        "SignedHornerRoot",
        "SignedHornerValueDerivative",
        "SignedNonsingularHornerRoot",
        "SignedSimpleHornerRoot",
        "SimpleHornerRoot"
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt"
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      "dependents": [],
      "expansion": "∀ sph_i_secondwave. ∀ sph_A_secondwave. ∀ sph_B_secondwave. ∀ sph_C_secondwave. Lt(sph_i_secondwave,l) → BetaAt(pb,pc,sph_i_secondwave,sph_A_secondwave) → BetaAt(nb,nc,sph_i_secondwave,sph_B_secondwave) → BetaAt(gb,gc,sph_i_secondwave,sph_C_secondwave) → sph_C_secondwave = sph_A_secondwave + h · sph_B_secondwave",
      "expansion_sha256": "298ccb982737b70cc8f378ca3c14b0c5f1d0cdda53c9c8bbb82b136e1bb0b545",
      "meaning": "Every actual coefficient in the new code is the positive coefficient plus h times the negative coefficient.",
      "milestone_users": [
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      "name": "HornerCoefficientBlend",
      "parameters": [
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        "nb",
        "nc",
        "gb",
        "gc",
        "h",
        "l"
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        "blueprint_name": "HornerCoefficientBlend",
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        "reviewed_id": "ND0081",
        "reviewed_name": "HornerCoefficientBlend",
        "reviewed_parameters": [
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          "nc",
          "gb",
          "gc",
          "h",
          "l"
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        "route": "hensel-lifting"
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      "topological_layer": 1,
      "transitive_dependencies": [
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    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt"
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      "dependents": [
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      "expansion": "Beta(u,v,0,0) ∧ Beta(d,e,0,0) ∧ ∀i. Lt(i,l) → ∃a q q1 h h1. Beta(b,c,i,a) ∧ Beta(u,v,i,q) ∧ Beta(u,v,i+1,q1) ∧ Beta(d,e,i,h) ∧ Beta(d,e,i+1,h1) ∧ q1=q*t+a ∧ h1=h*t+q",
      "expansion_sha256": "15f16a83525094721a687beef5723de5fc0c24c04dd8160aedaac4a09dfd91cb",
      "meaning": "A pair of coupled beta-coded Horner traces computing both a natural polynomial and its exact formal derivative.",
      "milestone_users": [
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      "name": "HornerDerivativeTrace",
      "parameters": [
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        "l",
        "u",
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        "d",
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        "blueprint_name": "HornerDerivativeTrace",
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        "route": "polynomial-hensel"
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      "topological_layer": 1,
      "transitive_dependencies": [
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      "transitive_dependents": [
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        "HornerDerivativeOnly",
        "HornerTaylorRemainder",
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        "SignedNonsingularHornerRoot",
        "SignedSimpleHornerRoot",
        "SimpleHornerRoot"
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      "dependencies": [
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      "dependents": [
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      "expansion": "∀ mdr_i_secondwave. Lt(mdr_i_secondwave,l) → BetaAt(b,c,mdr_i_secondwave,mdr_i_secondwave)",
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      "meaning": "The actual beta-decoded coordinate list 0,1,…,l−1; its boundedness, injectivity, and full-matrix selection are proved separately.",
      "milestone_users": [
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      "name": "IdentityMatrixSelector",
      "parameters": [
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      "reviewed_match": {
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        "reviewed_id": "ND0141",
        "reviewed_name": "IdentityMatrixSelector",
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      "dependencies": [
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      "expansion": "∀ fp_i_defined_injective_prefix. ∀ fp_j_defined_injective_prefix. ∀ fp_value_defined_injective_prefix. Lt(fp_i_defined_injective_prefix,l) → Lt(fp_j_defined_injective_prefix,l) → BetaAt(b,c,fp_i_defined_injective_prefix,fp_value_defined_injective_prefix) → BetaAt(b,c,fp_j_defined_injective_prefix,fp_value_defined_injective_prefix) → fp_i_defined_injective_prefix = fp_j_defined_injective_prefix",
      "expansion_sha256": "bf790f23086a6c34d253452a8c56b5ddb4e044e4c40f07219d5a5f367cc4e5dc",
      "meaning": "Equal decoded values below l have equal indices.",
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      "parameters": [
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        "reviewed_id": "PD0025",
        "reviewed_name": "InjectivePrefix",
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        "route": "quadratic-reciprocity"
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      "transitive_dependents": [
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "∀ ics_index_secondwave. ∀ ics_value0_secondwave. ∀ ics_value1_secondwave. ∀ ics_value2_secondwave. ∀ ics_value3_secondwave. ∀ ics_value4_secondwave. ∀ ics_value5_secondwave. Lt(ics_index_secondwave,l) → BetaAt(ab,ac,ics_index_secondwave,ics_value0_secondwave) → BetaAt(db,dc,ics_index_secondwave,ics_value1_secondwave) → BetaAt(eb,ec,ics_index_secondwave,ics_value2_secondwave) → BetaAt(fb,fc,ics_index_secondwave,ics_value3_secondwave) → BetaAt(pb,pc,ics_index_secondwave,ics_value4_secondwave) → BetaAt(nb,nc,ics_index_secondwave,ics_value5_secondwave) → ics_value4_secondwave + (ics_value1_secondwave + ics_value3_secondwave) = ics_value0_secondwave + ics_value2_secondwave + ics_value5_secondwave",
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      "meaning": "Actual coordinatewise addition of represented signed integers, expressed without subtraction or a preferred pair representation.",
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      "name": "IntegerVectorAdd",
      "parameters": [
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        "pb",
        "pc",
        "nb",
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      "dependents": [
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      "expansion": "∀ ics_index_secondwave. ∀ ics_value0_secondwave. ∀ ics_value1_secondwave. ∀ ics_value2_secondwave. ∀ ics_value3_secondwave. Lt(ics_index_secondwave,l) → BetaAt(ab,ac,ics_index_secondwave,ics_value0_secondwave) → BetaAt(db,dc,ics_index_secondwave,ics_value1_secondwave) → BetaAt(eb,ec,ics_index_secondwave,ics_value2_secondwave) → BetaAt(fb,fc,ics_index_secondwave,ics_value3_secondwave) → ics_value0_secondwave + ics_value3_secondwave = ics_value2_secondwave + ics_value1_secondwave",
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      "dependencies": [
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      "expansion": "∀ ics_index_secondwave. ∀ ics_value0_secondwave. ∀ ics_value1_secondwave. Lt(ics_index_secondwave,l) → BetaAt(ab,ac,ics_index_secondwave,ics_value0_secondwave) → BetaAt(db,dc,ics_index_secondwave,ics_value1_secondwave) → ics_value0_secondwave = ics_value1_secondwave",
      "expansion_sha256": "a522f5d117d9bc1724bae55e5bf707f38a5e14939526101b905a7631a9a70b10",
      "meaning": "Every actual positive component equals its negative component, so each represented integer is zero.",
      "milestone_users": [
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      "name": "IntegerVectorZero",
      "parameters": [
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      "expansion": "(Even(m) ∧ Odd(n)) ∨ (Odd(m) ∧ Even(n))",
      "expansion_sha256": "557680da074b44346495c97dc40add024727b00ad2c8641bcebdbc6a5f31b2b5",
      "meaning": "A witnessed disjunction of the two opposite-parity orientations.",
      "milestone_users": [
        "G077"
      ],
      "name": "OppositeParity",
      "parameters": [
        "m",
        "n"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "OppositeParity",
        "blueprint_parameters": [
          "m",
          "n"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "84c8359d58447b9b813f54e27586f1c66dac8b59a964f6cc686b90d9d5bd7b3a",
        "reviewed_id": "CF0016",
        "reviewed_name": "OppositeParity",
        "reviewed_parameters": [
          "m",
          "n"
        ],
        "route": "pythagorean-fermat-four"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "Even",
        "Odd"
      ],
      "transitive_dependents": [
        "EuclidParameters",
        "EuclidParametrization"
      ]
    },
    {
      "arity": 11,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "NaturalPair"
      ],
      "dependents": [
        "PerfectPowerProfileData"
      ],
      "expansion": "∃ ppf_code_0_prioritylayer. ∃ ppf_code_1_prioritylayer. ∃ ppf_code_2_prioritylayer. ∃ ppf_code_3_prioritylayer. ∃ ppf_code_4_prioritylayer. ∃ ppf_code_5_prioritylayer. ∃ ppf_code_6_prioritylayer. ∃ ppf_code_7_prioritylayer. NaturalPair(w,pb,ppf_code_0_prioritylayer) ∧ (NaturalPair(ppf_code_0_prioritylayer,pc,ppf_code_1_prioritylayer) ∧ (NaturalPair(ppf_code_1_prioritylayer,eb,ppf_code_2_prioritylayer) ∧ (NaturalPair(ppf_code_2_prioritylayer,ec,ppf_code_3_prioritylayer) ∧ (NaturalPair(ppf_code_3_prioritylayer,vb,ppf_code_4_prioritylayer) ∧ (NaturalPair(ppf_code_4_prioritylayer,vc,ppf_code_5_prioritylayer) ∧ (NaturalPair(ppf_code_5_prioritylayer,l,ppf_code_6_prioritylayer) ∧ (NaturalPair(ppf_code_6_prioritylayer,g,ppf_code_7_prioritylayer) ∧ NaturalPair(ppf_code_7_prioritylayer,rb,rc))))))))",
      "expansion_sha256": "719b12deb2582a8f60b775ec2c506ee68d529ad4e101b1d455dd812888671e0f",
      "meaning": "A real nested historical pair code stores the seven support fields, exponent gcd, and two root-table codes.",
      "milestone_users": [],
      "name": "PerfectPowerProfileCode",
      "parameters": [
        "w",
        "pb",
        "pc",
        "eb",
        "ec",
        "vb",
        "vc",
        "l",
        "g",
        "rb",
        "rc"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PerfectPowerProfileCode",
        "blueprint_parameters": [
          "w",
          "pb",
          "pc",
          "eb",
          "ec",
          "vb",
          "vc",
          "l",
          "g",
          "rb",
          "rc"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "reviewed_expansion_sha256": "bfb67d4edf8ab006da42e24269a345285f02a0b49bed7df02dfa265a96196c44",
        "reviewed_id": "ND0193",
        "reviewed_name": "PerfectPowerProfileCode",
        "reviewed_parameters": [
          "w",
          "pb",
          "pc",
          "eb",
          "ec",
          "vb",
          "vc",
          "l",
          "g",
          "rb",
          "rc"
        ],
        "route": "squarefree-kernels"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "NaturalPair"
      ],
      "transitive_dependents": [
        "PerfectPowerProfileData",
        "PowerProfile"
      ]
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "Dvd",
        "Pow"
      ],
      "dependents": [
        "PerfectPowerProfileData"
      ],
      "expansion": "∀ ppf_table_degree_prioritylayer. ¬ppf_table_degree_prioritylayer = 0 → Dvd(ppf_table_degree_prioritylayer,g) → ∃ x. BetaAt(b,c,ppf_table_degree_prioritylayer,x) ∧ Pow(x,ppf_table_degree_prioritylayer,n)",
      "expansion_sha256": "6e6df9f35769298504daace5d1a1e6b7f3652dd9b50a8cdeed11d85a4c3a6bd0",
      "meaning": "For each positive divisor k of g, the table actually decodes a root r with Pow(r,k,n). It is constructed after the root-existence proof.",
      "milestone_users": [],
      "name": "PerfectPowerRootTable",
      "parameters": [
        "n",
        "g",
        "b",
        "c"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PerfectPowerRootTable",
        "blueprint_parameters": [
          "n",
          "g",
          "b",
          "c"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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          1,
          2,
          3
        ],
        "reviewed_expansion_sha256": "fed0dc1794f15c8b23c10032ea7b504da025ce33d95c72161da59890e65ef657",
        "reviewed_id": "ND0192",
        "reviewed_name": "PerfectPowerRootTable",
        "reviewed_parameters": [
          "n",
          "g",
          "b",
          "c"
        ],
        "route": "squarefree-kernels"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "BetaAt",
        "Dvd",
        "Pow"
      ],
      "transitive_dependents": [
        "PerfectPowerProfileData",
        "PowerProfile"
      ]
    },
    {
      "arity": 6,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "Lt"
      ],
      "dependents": [
        "FpPolynomialTrim"
      ],
      "expansion": "∀ pftrim_index_polynomial_division_definition. ∀ pftrim_value_polynomial_division_definition. Lt(pftrim_index_polynomial_division_definition,M) → BetaAt(b,c,t + pftrim_index_polynomial_division_definition,pftrim_value_polynomial_division_definition) → BetaAt(d,e,pftrim_index_polynomial_division_definition,pftrim_value_polynomial_division_definition)",
      "expansion_sha256": "db2695eff4de59bfbb2c5c956b75e356ba45d6bf29095a3f03bfe252f4d6bf28",
      "meaning": "For every i<M and actual source value at t+i, the target beta prefix records that same value at i. No coefficient bound, primality, total input length, zero-prefix condition or suffix construction is assumed. The affine-slice construction theorem is not itself a definition-expansion edge.",
      "milestone_users": [
        "G091"
      ],
      "name": "PolynomialSuffix",
      "parameters": [
        "b",
        "c",
        "t",
        "d",
        "e",
        "M"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PolynomialSuffix",
        "blueprint_parameters": [
          "b",
          "c",
          "t",
          "d",
          "e",
          "M"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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          2,
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          4,
          5
        ],
        "reviewed_expansion_sha256": "51cca139708f3b222ada40b6ca6e6d2336241373bf862b3e2a69dd9f5cc2809e",
        "reviewed_id": "ND0329",
        "reviewed_name": "PolynomialSuffix",
        "reviewed_parameters": [
          "b",
          "c",
          "t",
          "d",
          "e",
          "M"
        ],
        "route": "polynomial-division-prerequisites"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "BetaAt",
        "Lt"
      ],
      "transitive_dependents": [
        "FpPolynomialTrim"
      ]
    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Pow"
      ],
      "dependents": [
        "BitLen"
      ],
      "expansion": "Pow(2,e,p)",
      "expansion_sha256": "96aa38d4bd34c29b36a0d745614252575b63617bc54fcc54b5a162f196024ff8",
      "meaning": "The exact constructive power-of-two graph.",
      "milestone_users": [
        "G022",
        "G027",
        "G101",
        "G102"
      ],
      "name": "PowTwo",
      "parameters": [
        "e",
        "p"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PowTwo",
        "blueprint_parameters": [
          "e",
          "p"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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          1
        ],
        "reviewed_expansion_sha256": "25c621e42d9363777853c7779bf06948571e8c1f072a8b6743d03fe6adb43033",
        "reviewed_id": "ND0028",
        "reviewed_name": "PowTwo",
        "reviewed_parameters": [
          "e",
          "p"
        ],
        "route": "binary-length"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "Pow"
      ],
      "transitive_dependents": [
        "BinaryCanonicalExponentDigitCode",
        "BinaryCompleteModularExecution",
        "BitLen",
        "EuclideanLogarithmicExecution"
      ]
    },
    {
      "arity": 7,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Pow"
      ],
      "dependents": [],
      "expansion": "a = b + d ∧ (Pow(a,n,A) ∧ (Pow(b,n,B) ∧ A = B + d · q))",
      "expansion_sha256": "45b74b749886da8697b6ddb6a263561047354449b60399a8243df478e04b082a",
      "meaning": "Actual powers A=a^n, B=b^n and balances a=b+d, A=B+dq. No prime, valuation, or LTE conclusion is assumed.",
      "milestone_users": [],
      "name": "PowerDifferenceQuotient",
      "parameters": [
        "a",
        "b",
        "n",
        "A",
        "B",
        "d",
        "q"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PowerDifferenceQuotient",
        "blueprint_parameters": [
          "a",
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          "n",
          "A",
          "B",
          "d",
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        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "d0ad9080e8a09e4eefe3be05d8c4728e596621775a906a4c50c75de73cc9753c",
        "reviewed_id": "ND0196",
        "reviewed_name": "PowerDifferenceQuotient",
        "reviewed_parameters": [
          "a",
          "b",
          "n",
          "A",
          "B",
          "d",
          "q"
        ],
        "route": "exponent-lifting"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "Pow"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 11,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Pow"
      ],
      "dependents": [],
      "expansion": "Pow(a,S S k,A) ∧ (Pow(b,S S k,B) ∧ (Pow(b,S k,R) ∧ (Pow(b,k,T) ∧ (A = B + d · Q ∧ (Q = S S k · R + d · C ∧ 2 · C = S S k · S k · T + d · H)))))",
      "expansion_sha256": "cb6082fc144087db5d069c33b61e603c4c0c8cd92418735d9e1b106109849159",
      "meaning": "Four actual powers at exponents k+2,k+1,k and three subtraction-free difference/correction balances. Ordinary induction constructs all seven witnesses.",
      "milestone_users": [],
      "name": "PowerDifferenceSecondOrder",
      "parameters": [
        "a",
        "b",
        "d",
        "k",
        "A",
        "B",
        "R",
        "T",
        "Q",
        "C",
        "H"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PowerDifferenceSecondOrder",
        "blueprint_parameters": [
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          "k",
          "A",
          "B",
          "R",
          "T",
          "Q",
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        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "505932f742f37fc4f903a2fac044f62e45614bb193dec37a57743ec28127976a",
        "reviewed_id": "ND0197",
        "reviewed_name": "PowerDifferenceSecondOrder",
        "reviewed_parameters": [
          "a",
          "b",
          "d",
          "k",
          "A",
          "B",
          "R",
          "T",
          "Q",
          "C",
          "H"
        ],
        "route": "exponent-lifting"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "Pow"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Dvd",
        "Pow"
      ],
      "dependents": [
        "BoundedPowerValuation"
      ],
      "expansion": "∃ bpv_result_bertrand_defined_power_divides. Pow(p,e,bpv_result_bertrand_defined_power_divides) ∧ Dvd(bpv_result_bertrand_defined_power_divides,n)",
      "expansion_sha256": "72186fa4c4f6b4d2269b42150878bea8b7b3c68d22d8812d3a8ca85965bc791c",
      "meaning": "The relational power p to exponent e divides n.",
      "milestone_users": [
        "G035"
      ],
      "name": "PowerDivides",
      "parameters": [
        "p",
        "e",
        "n"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PowerDivides",
        "blueprint_parameters": [
          "p",
          "e",
          "n"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "6751b0ca7d1b4cfe36e4fdf2c0c2c18aa046a9f1a4a47d49db778c4677d866a3",
        "reviewed_id": "PD0044",
        "reviewed_name": "PowerDivides",
        "reviewed_parameters": [
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          "e",
          "n"
        ],
        "route": "bertrand-postulate"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "Dvd",
        "Pow"
      ],
      "transitive_dependents": [
        "BetaValuationPrefix",
        "BoundedPowerValuation",
        "EulerProduct",
        "LiftedPowerDifference",
        "PerfectPowerProfileData",
        "PowerProfile",
        "PrimeExponentEntries",
        "PrimePowerValuation",
        "PrimeValuationSupport",
        "PrimeValuationsDivisible"
      ]
    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "DivRem",
        "Lt",
        "Pow"
      ],
      "dependents": [
        "BinaryColumnCarryCount"
      ],
      "expansion": "∀ bls_index_bertrand_defined_power_quotients. Lt(bls_index_bertrand_defined_power_quotients,l) → ∃ x. ∃ y. ∃ z. Pow(p,S bls_index_bertrand_defined_power_quotients,x) ∧ (BetaAt(b,c,bls_index_bertrand_defined_power_quotients,y) ∧ DivRem(n,x,y,z))",
      "expansion_sha256": "91a68f54097239f70a5ba0d4cdbcce206146b54284e74ad9961cd02dc7e3f6b2",
      "meaning": "The beta-coded prefix stores the quotients of n by the first l positive powers of p.",
      "milestone_users": [
        "G035"
      ],
      "name": "PowerQuotPrefix",
      "parameters": [
        "p",
        "n",
        "b",
        "c",
        "l"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "PowerQuotPrefix",
        "blueprint_parameters": [
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          "n",
          "b",
          "c",
          "l"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "c89e442b76a056c8831e994d78c9555d48565d665ea51e69b7fe9eda31ded290",
        "reviewed_id": "PD0049",
        "reviewed_name": "PowerQuotPrefix",
        "reviewed_parameters": [
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          "n",
          "b",
          "c",
          "l"
        ],
        "route": "bertrand-postulate"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
        "BetaAt",
        "DivRem",
        "Lt",
        "Pow"
      ],
      "transitive_dependents": [
        "BinaryColumnCarryCount",
        "CarryCountMany",
        "MultinomialCarryPrefix"
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    },
    {
      "arity": 1,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Dvd"
      ],
      "dependents": [
        "AllPrime",
        "AllRootLifts",
        "BertrandWindow",
        "CornacchiaRoot",
        "ECCount",
        "EulerPrimePowerFactor",
        "Factorization",
        "FiniteField",
        "FpElement",
        "GaussBit",
        "HasPrimeSquareDivisor",
        "Irred",
        "NextPrime",
        "PrimeBitPrefix",
        "PrimeDivisorSupport",
        "PrimeExponentEntries",
        "PrimePowerValuation",
        "PrimeThreeModFourDivisor",
        "PrimeValuationsDivisible",
        "PrimitiveRootModulus",
        "Primorial",
        "QuadBit",
        "SimpleLift",
        "Squarefree",
        "TeichLift",
        "Val",
        "WeierstrassCertificate"
      ],
      "expansion": "p>1 ∧ ∀ d<p. Dvd(d,p) → d=1",
      "expansion_sha256": "b7124d08a14bed2c66c29bde816efcd0d062e3f580b590bf87325f8874b8b567",
      "meaning": "A natural prime.",
      "milestone_users": [
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        "T09",
        "A02",
        "A04",
        "A05",
        "A07",
        "G017",
        "G021",
        "G023",
        "G024",
        "G025",
        "G026",
        "G027",
        "G028",
        "G030",
        "G032",
        "G033",
        "G034",
        "G035",
        "G037",
        "G038",
        "G039",
        "G040",
        "G041",
        "G042",
        "G044",
        "G046",
        "G050",
        "G051",
        "G053",
        "G054",
        "G056",
        "G058",
        "G061",
        "G062",
        "G083",
        "G086",
        "G089",
        "G091",
        "G095",
        "G096",
        "G097",
        "G098",
        "G099",
        "G100",
        "G103",
        "G104",
        "G105",
        "G106",
        "G107",
        "G110",
        "G112",
        "G114",
        "G119"
      ],
      "name": "Prime",
      "parameters": [
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      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "Prime",
        "blueprint_parameters": [
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        "reviewed_expansion_sha256": "62f78d205c303365b156144e260330ee3fd0798bb85f15e76eb44215d7759979",
        "reviewed_id": "PD0004",
        "reviewed_name": "Prime",
        "reviewed_parameters": [
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        "route": "quadratic-reciprocity"
      },
      "topological_layer": 1,
      "transitive_dependencies": [
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      ],
      "transitive_dependents": [
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        "AllRootLifts",
        "BertrandChain",
        "BertrandWindow",
        "CornacchiaRoot",
        "CornacchiaStateInvariant",
        "CornacchiaTrace",
        "ECCount",
        "EulerFactorPrefix",
        "EulerPrimePowerFactor",
        "EulerProduct",
        "FactorParitySign",
        "FactorialValuation",
        "Factorization",
        "FiniteField",
        "FpElement",
        "GaussBit",
        "HasPrimeSquareDivisor",
        "InitialPrimeChain",
        "InitialPrimeList",
        "Irred",
        "NaturalSquarefreeDecomposition",
        "NextPrime",
        "PerfectPowerProfileData",
        "PowerProfile",
        "PowerValuation",
        "PowerValuationOne",
        "PrimeBitPrefix",
        "PrimeDivisorSupport",
        "PrimeExponentEntries",
        "PrimeFactorList",
        "PrimePowerValuation",
        "PrimeThreeModFourDivisor",
        "PrimeValuationSupport",
        "PrimeValuationsDivisible",
        "PrimitiveRootModulus",
        "Primorial",
        "QuadBit",
        "SimpleLift",
        "Squarefree",
        "TeichLift",
        "Val",
        "WeierstrassCertificate"
      ]
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "Dvd",
        "Lt"
      ],
      "dependents": [
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      ],
      "expansion": "(∀ x. ∀ y. Lt(x,l) → BetaAt(b,c,x,y) → Dvd(g,y)) ∧ (∀ x. (∀ y. ∀ z. Lt(y,l) → BetaAt(b,c,y,z) → Dvd(x,z)) → Dvd(x,g))",
      "expansion_sha256": "b9ffdb0573e1c02adfac5eded9a06371a8667eeaece58b4eeecb9a7b341d6334",
      "meaning": "g divides every actual decoded exponent, and every common divisor of these exponents divides g. The empty-prefix gcd is zero.",
      "milestone_users": [],
      "name": "PrimeExponentPrefixGCD",
      "parameters": [
        "b",
        "c",
        "l",
        "g"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "PrimeExponentPrefixGCD",
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        "kind": "exact-name",
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        "reviewed_id": "ND0191",
        "reviewed_name": "PrimeExponentPrefixGCD",
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        "route": "squarefree-kernels"
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      "topological_layer": 1,
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      "transitive_dependents": [
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    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      ],
      "dependents": [
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      ],
      "expansion": "¬Dvd(p,d) ∧ e = p · d ∨ (d = p · e ∧ ¬Dvd(p,e) ∨ Dvd(p · p,d) ∧ e = d)",
      "expansion_sha256": "5f803bf45a0b9b5753f0fff950cacd583f851b7f0a74dfd4e4aa28d7c4506d01",
      "meaning": "Add a fresh factor p, remove a single factor p with p-free quotient, or fix a multiple of p squared. The graph contains no Möbius sign or cancellation hypothesis.",
      "milestone_users": [],
      "name": "PrimeFactorToggle",
      "parameters": [
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "PrimeFactorToggle",
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        "reviewed_id": "ND0283",
        "reviewed_name": "PrimeFactorToggle",
        "reviewed_parameters": [
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        "route": "mobius-divisor-cancellation"
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      "topological_layer": 1,
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      "transitive_dependents": [
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    },
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      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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        "Multinomial",
        "PrimeFactorList",
        "PrimeValuationSupport",
        "Primorial"
      ],
      "expansion": "∃ ff_u_defined_product. ∃ ff_v_defined_product. BetaAt(ff_u_defined_product,ff_v_defined_product,0,1) ∧ (BetaAt(ff_u_defined_product,ff_v_defined_product,l,z) ∧ (∀ x. Lt(x,l) → ∃ y. ∃ n. ∃ m. BetaAt(b,c,x,y) ∧ (BetaAt(ff_u_defined_product,ff_v_defined_product,x,n) ∧ (BetaAt(ff_u_defined_product,ff_v_defined_product,S x,m) ∧ m = n · y))))",
      "expansion_sha256": "4aa178da7b3255e83fd7bc06b03e05d4de7d26bcab7587ef6e22b98d5b08628f",
      "meaning": "z is the product of a beta-coded prefix of length l.",
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        "G035",
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      "name": "Product",
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        "reviewed_id": "PD0014",
        "reviewed_name": "Product",
        "reviewed_parameters": [
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        "route": "quadratic-reciprocity"
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      "topological_layer": 1,
      "transitive_dependencies": [
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      "transitive_dependents": [
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        "PrimeFactorList",
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        "Primorial"
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    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "∃ qr_x_defined_qres. ModEq(m,qr_x_defined_qres · qr_x_defined_qres,a)",
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      "meaning": "a has a square root modulo m.",
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        "reviewed_expansion_sha256": "e272443fa880570bd29f01bba5a3f2bf90c8475a2eb2f92ce659ce165916c8db",
        "reviewed_id": "PD0021",
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        "route": "quadratic-reciprocity"
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    {
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      "dependencies": [
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      ],
      "dependents": [
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      ],
      "expansion": "∀ ff_i_defined_range. Lt(ff_i_defined_range,l) → BetaAt(b,c,ff_i_defined_range,a + ff_i_defined_range)",
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      "meaning": "The decoded prefix is a,a+1,...,a+l-1.",
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        "reviewed_expansion_sha256": "b04a3e6b152775815605b45421d89e1e346757c9a1c7cb86290c98e5a42f18b9",
        "reviewed_id": "PD0018",
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        "route": "quadratic-reciprocity"
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    },
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      "authority": "blueprint-vocabulary-only",
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      "expansion": "NaturalAbsDifference(a · t + b · rn,b · rp,E)",
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      "meaning": "The exact cross-product error |a·t−b·(rp−rn)| for an arbitrary signed numerator. This is not an approximation inequality.",
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      "name": "RationalApproximationError",
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        "reviewed_id": "ND0199",
        "reviewed_name": "RationalApproximationError",
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        "route": "best-approximation"
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    {
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      "dependencies": [
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      "dependents": [],
      "expansion": "∀ ff_i_defined_repeat. Lt(ff_i_defined_repeat,l) → BetaAt(b,c,ff_i_defined_repeat,a)",
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      "meaning": "The decoded prefix repeats a for l positions.",
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        "route": "quadratic-reciprocity"
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    {
      "arity": 8,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "p + N · qn + en = n + N · qp + ep ∧ (SignedDifferenceSquare(ep,en,t · t) ∧ Le(t + t,N))",
      "expansion_sha256": "91834fe741b7858dfad7a381aa02663346e06980a819e7b0de1a054e42aeb53b",
      "meaning": "A genuine signed quotient and signed error represent p−n=N·(qp−qn)+(ep−en), with absolute error t and 2t≤N.",
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      "name": "RoundedSignedDivision",
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        "route": "gaussian-integers"
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      "expansion": "∃ sa_lp_lowerlayer. ∃ sa_ln_lowerlayer. ∃ sa_rp_lowerlayer. ∃ sa_rn_lowerlayer. ∃ sa_op_lowerlayer. ∃ sa_on_lowerlayer. SignedDecode(a,sa_lp_lowerlayer,sa_ln_lowerlayer) ∧ (SignedDecode(b,sa_rp_lowerlayer,sa_rn_lowerlayer) ∧ (SignedDecode(c,sa_op_lowerlayer,sa_on_lowerlayer) ∧ sa_lp_lowerlayer + sa_rp_lowerlayer + sa_on_lowerlayer = sa_ln_lowerlayer + sa_rn_lowerlayer + sa_op_lowerlayer))",
      "expansion_sha256": "dc3548d4ffaf0095ef76dba03d763975c7113587c497651509a61e16d3780e54",
      "meaning": "Actual addition of original canonical signed codes, witnessed by their decoders and balanced equality.",
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      "name": "SignedAdd",
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        "route": "arithmetic-foundations"
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    {
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      "dependencies": [
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      "dependents": [
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      "expansion": "(Even(i) ∧ p=ap*bp+an*bn ∧ n=ap*bn+an*bp) ∨ (Odd(i) ∧ p=ap*bn+an*bp ∧ n=ap*bp+an*bn)",
      "expansion_sha256": "2f9d829f1309a23e8371f149573c950f8d15c2e206daf0efad878f42442a3b45",
      "meaning": "The exact subtraction-free positive and negative components of the signed product multiplied by the parity sign (-1)^i.",
      "milestone_users": [
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      "name": "SignedAlternatingCofactorTerm",
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      "transitive_dependents": [
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        "SignedAlternatingProductPrefix",
        "SignedDeterminantHistory",
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        "SignedEvaluatedCofactors",
        "SignedFirstRowCofactorFold",
        "SignedRecursiveDeterminant",
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    },
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      "expansion": "∃ sb_pos_lowerlayer. ∃ sb_neg_lowerlayer. SignedDecode(z,sb_pos_lowerlayer,sb_neg_lowerlayer) ∧ p + sb_neg_lowerlayer = n + sb_pos_lowerlayer",
      "expansion_sha256": "ce76db8373028b4a63794564b29cef2e816cfea32ecee72a259f7ed270902510",
      "meaning": "The original canonical code z represents the integer difference p−n; these supplied components need not be normalized.",
      "milestone_users": [],
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        "route": "arithmetic-foundations"
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      "transitive_dependents": [
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        "ArithRowSums",
        "ArithScale",
        "ArithSlice",
        "ArithTable",
        "ArithTableEqual",
        "ConstantOneTable",
        "DirichletCoprimeProductData",
        "DirichletDivisorGridWitness",
        "DirichletEntry",
        "DirichletFactorRow",
        "DirichletFlatEntry",
        "DirichletFlatPrefix",
        "DirichletGrid",
        "DirichletGridEntry",
        "DirichletInverse",
        "DirichletPrefix",
        "DirichletSum",
        "DirichletTable",
        "DirichletUnitAtOne",
        "DivisorMask",
        "DivisorMaskEntry",
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        "DivisorTransform",
        "EDivRem",
        "EEuclideanDivision",
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        "GAllIrreducible",
        "GAllPrime",
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        "GEuclideanDivision",
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        "GFactorPermutation",
        "GGcd",
        "GIrreducible",
        "GIrreducibleFactorization",
        "GMatchedFactors",
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        "GPrimeFactorization",
        "GProduct",
        "GProductStep",
        "GProductSteps",
        "GProperNormDivisor",
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        "GUnit",
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        "SignedIncidenceEntry",
        "SignedIncidenceFlatEntry",
        "SignedIncidenceFlatPrefix",
        "SignedPrefixSum",
        "SignedRectangularSum",
        "SignedSliceSum",
        "SignedSupportIncidence",
        "SignedSupportReindex",
        "SignedWeightedSum",
        "SignedZeroWindow",
        "ZPairAdd",
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    },
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "∀ cfc_numerator_prioritylayer. ∀ cfc_negative_numerator_prioritylayer. ∀ cfc_denominator_prioritylayer. ∀ cfc_current_error_prioritylayer. ∀ cfc_candidate_error_prioritylayer. ¬cfc_denominator_prioritylayer = 0 → Lt(cfc_denominator_prioritylayer,v) → NaturalAbsDifference(a · v,b · u,cfc_current_error_prioritylayer) → NaturalAbsDifference(a · cfc_denominator_prioritylayer + b · cfc_negative_numerator_prioritylayer,b · cfc_numerator_prioritylayer,cfc_candidate_error_prioritylayer) → Le(cfc_current_error_prioritylayer,cfc_candidate_error_prioritylayer)",
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      "meaning": "The same second-kind comparison for every signed numerator rp−rn and every 0<t<v; it includes the natural comparison as a corollary.",
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      "name": "SignedBestApproximationSecondKind",
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      ],
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        "reviewed_expansion_sha256": "47a7591915461c69d675f5b1938536fd09e2b58743f8d6292f4e631f6ad21bdc",
        "reviewed_id": "ND0207",
        "reviewed_name": "SignedBestApproximationSecondKind",
        "reviewed_parameters": [
          "a",
          "b",
          "u",
          "v"
        ],
        "route": "best-approximation"
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      "topological_layer": 1,
      "transitive_dependencies": [
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        "Lt",
        "NaturalAbsDifference"
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      "transitive_dependents": []
    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "∃ sbz_xp_lowerlayer. ∃ sbz_xn_lowerlayer. ∃ sbz_yp_lowerlayer. ∃ sbz_yn_lowerlayer. SignedDecode(u,sbz_xp_lowerlayer,sbz_xn_lowerlayer) ∧ (SignedDecode(v,sbz_yp_lowerlayer,sbz_yn_lowerlayer) ∧ a · sbz_xp_lowerlayer + b · sbz_yp_lowerlayer = g + (a · sbz_xn_lowerlayer + b · sbz_yn_lowerlayer))",
      "expansion_sha256": "4e1da3ffaee7ad0fa63539130561c1c4d0984825e9b647c6ad95aa6744f0fd31",
      "meaning": "The original signed coefficient codes u and v witness a·u+b·v=g by actual decoded balanced arithmetic.",
      "milestone_users": [
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      "name": "SignedBezout",
      "parameters": [
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        "b",
        "u",
        "v"
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      "reviewed_incompatibility": null,
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        "reviewed_name": "SignedBezout",
        "reviewed_parameters": [
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          "a",
          "b",
          "u",
          "v"
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        "route": "arithmetic-foundations"
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      "transitive_dependents": []
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    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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      "expansion": "¬ModEq(p,dp,dn)",
      "expansion_sha256": "6b6596f431f3409b6124736057ce05aae25f1578e56a94a7e654934fe00a6b58",
      "meaning": "The actual signed derivative dp−dn is not congruent to zero modulo p; no inverse is supplied.",
      "milestone_users": [
        "G095"
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      "name": "SignedDerivativeNonzero",
      "parameters": [
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        "dp",
        "dn"
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "reviewed_id": "ND0126",
        "reviewed_name": "SignedDerivativeNonzero",
        "reviewed_parameters": [
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        "route": "hensel-lifting"
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    {
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      "dependencies": [
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      "dependents": [
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      "expansion": "∃ sph_inverse_secondwave. Lt(sph_inverse_secondwave,p) ∧ ModEq(p,dp · sph_inverse_secondwave,1 + dn · sph_inverse_secondwave)",
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      "meaning": "An actual bounded inverse of dp−dn modulo p, expressed by balanced congruence.",
      "milestone_users": [
        "G095"
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      "name": "SignedDerivativeUnit",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "route": "hensel-lifting"
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      "transitive_dependents": [
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    },
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      "dependencies": [
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      "dependents": [
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        "SignedDeterminantHistory",
        "SignedRecursiveDeterminant"
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      "expansion": "∃ mdr_z_secondwave. SignedDeterminantNodeCode(mdr_z_secondwave,d,pb,pc,nb,nc,p,n) ∧ BetaAt(b,c,i,mdr_z_secondwave)",
      "expansion_sha256": "f22d780454d18e477ef6d27f636692c8428f48deedb4a0d811f03fe4278d747f",
      "meaning": "An actual determinant-node record decoded from a beta history.",
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      "name": "SignedDeterminantNodeAt",
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        "route": "integer-linear-algebra"
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      "expansion": "p + m · t = n + m · q + r ∧ Lt(r,m)",
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      "meaning": "The genuine signed floor equation (p−n)=m·(q−t)+r and strict natural remainder bound r<m.",
      "milestone_users": [],
      "name": "SignedFloor",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "reviewed_id": "ND0155",
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        "route": "gaussian-integers"
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "expansion": "(∀ x. ∀ y. Lt(x,d · d) → BetaAt(pb,pc,x,y) → BetaAt(qb,qc,x,y)) ∧ (∀ x. ∀ y. Lt(x,d · d) → BetaAt(nb,nc,x,y) → BetaAt(rb,rc,x,y))",
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      "meaning": "Pointwise equality of both actual component streams of two square matrices; this is stronger than equality only of their signed differences.",
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      "name": "SignedMatrixPrefixEquality",
      "parameters": [
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        "qb",
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        "d"
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      "reviewed_incompatibility": null,
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        "route": "integer-linear-algebra"
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      "dependents": [
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      "expansion": "∃ sm_lp_lowerlayer. ∃ sm_ln_lowerlayer. ∃ sm_rp_lowerlayer. ∃ sm_rn_lowerlayer. ∃ sm_op_lowerlayer. ∃ sm_on_lowerlayer. SignedDecode(a,sm_lp_lowerlayer,sm_ln_lowerlayer) ∧ (SignedDecode(b,sm_rp_lowerlayer,sm_rn_lowerlayer) ∧ (SignedDecode(c,sm_op_lowerlayer,sm_on_lowerlayer) ∧ sm_lp_lowerlayer · sm_rp_lowerlayer + sm_ln_lowerlayer · sm_rn_lowerlayer + sm_on_lowerlayer = sm_lp_lowerlayer · sm_rn_lowerlayer + sm_ln_lowerlayer · sm_rp_lowerlayer + sm_op_lowerlayer))",
      "expansion_sha256": "ecde243b490db5cc67d94d9e34b518933debe1d587c139352cd54bd5209eb68d",
      "meaning": "Actual multiplication of original canonical signed codes; opposite-sign products remain on the negative side of the balance.",
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        "route": "arithmetic-foundations"
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      "transitive_dependents": [
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      "arity": 2,
      "authority": "blueprint-vocabulary-only",
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      "dependents": [
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      "expansion": "∃ sn_pos_lowerlayer. ∃ sn_neg_lowerlayer. SignedDecode(a,sn_pos_lowerlayer,sn_neg_lowerlayer) ∧ SignedDecode(b,sn_neg_lowerlayer,sn_pos_lowerlayer)",
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      "meaning": "Canonical signed negation swaps the positive and negative decoded parts.",
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        "route": "arithmetic-foundations"
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      "dependencies": [
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      "dependents": [
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      "expansion": "(∀ x. Lt(x,q · q) → ∃ y. (∃ z. ∃ n. ∃ m. ∃ k. x = q · z + n ∧ (Lt(n,q) ∧ (BetaAt(rb,rc,z,m) ∧ (BetaAt(cb,cc,n,k) ∧ BetaAt(pb,pc,m · w + k,y))))) ∧ BetaAt(ub,uc,x,y)) ∧ (∀ x. Lt(x,q · q) → ∃ y. (∃ z. ∃ n. ∃ m. ∃ k. x = q · z + n ∧ (Lt(n,q) ∧ (BetaAt(rb,rc,z,m) ∧ (BetaAt(cb,cc,n,k) ∧ BetaAt(nb,nc,m · w + k,y))))) ∧ BetaAt(vb,vc,x,y))",
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      "meaning": "Every entry of both components of the q-by-q output is the actual row-major parent entry selected by the two coordinate streams.",
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      "name": "SignedSelectedSubmatrix",
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      "expansion": "FermatFourCounterexample(x,y,z) ∧ Lt(z,h)",
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        "route": "pythagorean-fermat-four"
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      "dependencies": [
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      "dependents": [],
      "expansion": "∀ dp_i. Lt(S dp_i,l) → ∃ x. ∃ y. BetaAt(b,c,dp_i,x) ∧ (BetaAt(b,c,S dp_i,y) ∧ Le(x,y))",
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      "meaning": "Adjacent decoded entries form a nondecreasing prefix.",
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        "reviewed_expansion_sha256": "7e619d4c39c1271470a2192db68824c0c8aad95013a11ddd8384dab121348680",
        "reviewed_id": "PD0029",
        "reviewed_name": "Sorted",
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        "route": "quadratic-reciprocity"
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      "dependencies": [
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      "dependents": [
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      "meaning": "The successor residues of i and j multiply to one modulo m.",
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      "reviewed_incompatibility": null,
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        "route": "quadratic-reciprocity"
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      "dependents": [
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      "expansion": "∀ fp_value_defined_surjective_prefix. Lt(fp_value_defined_surjective_prefix,l) → ∃ x. Lt(x,l) ∧ BetaAt(b,c,x,fp_value_defined_surjective_prefix)",
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        "route": "quadratic-reciprocity"
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    },
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      "dependencies": [
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      "dependents": [],
      "expansion": "¬T = 0 ∧ (∀ x. ∀ y. (∀ z. Lt(z,l) → ∃ n. BetaAt(x,y,z,n) ∧ Lt(n,B)) → ∃ z. Lt(z,T) ∧ (∀ n. ∀ m. Lt(n,l) → BetaAt(x,y,n,m) → BetaAt(z,c,n,m)))",
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      "meaning": "One fixed scale c and positive finite code bound T recode every actual length-l prefix with values below B; completeness is part of the relation.",
      "milestone_users": [
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      "parameters": [
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      "expansion": "m>1 ∧ ∃ b<m. Mod(a*b,1,m)",
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      "meaning": "A modular unit with inverse.",
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      "name": "Unit",
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      "dependencies": [
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      "expansion": "E has full rational 2-torsion, SelmerWitness(E,S), S is finite and computable, and iota witnesses an injection E(Q)/2E(Q)→S; no quotient image decision, coset representatives, or full Mordell–Weil generators are asserted",
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      "meaning": "Restricted weak Mordell–Weil finiteness by finite Selmer injection.",
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      "dependencies": [
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      "dependents": [],
      "expansion": "∃ ee_real_square_lowerlayer. ∃ ee_imag_square_lowerlayer. SignedDifferenceSquare(ap,an,ee_real_square_lowerlayer) ∧ (SignedDifferenceSquare(bp,bn,ee_imag_square_lowerlayer) ∧ n = ee_real_square_lowerlayer + 3 · ee_imag_square_lowerlayer)",
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      "meaning": "The witnessed sum (ap−an)²+3(bp−bn)². It supports the proved identity 4N(a+bω)=(2a−b)²+3b², not a new norm axiom.",
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        "route": "eisenstein-integers"
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      "dependencies": [
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      "dependents": [
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      "expansion": "∃ ge_real_code_lowerlayer. ∃ ge_imaginary_code_lowerlayer. z = (ge_real_code_lowerlayer + ge_imaginary_code_lowerlayer) · S (ge_real_code_lowerlayer + ge_imaginary_code_lowerlayer) + (ge_imaginary_code_lowerlayer + ge_imaginary_code_lowerlayer) ∧ (SignedDecode(ge_real_code_lowerlayer,ap,an) ∧ SignedDecode(ge_imaginary_code_lowerlayer,bp,bn))",
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      "meaning": "The shared injective code of two original canonical signed integers, with their normalized coordinate decoders. Both quadratic integer rings use this same carrier.",
      "milestone_users": [],
      "name": "ZPairDecode",
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        "route": "gaussian-integers"
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      "dependencies": [
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      "dependents": [
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      "expansion": "∀ dp_i. Lt(dp_i,l) → ∃ x. BetaAt(b,c,dp_i,x) ∧ Prime(x)",
      "expansion_sha256": "1b11d871189f33e1d122edb91ca332924fdcf7a3c3d2011073884659920a14bd",
      "meaning": "Every decoded factor below l is prime.",
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    },
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      "dependencies": [
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      "dependents": [],
      "expansion": "Prime(p),k>0 and S lists precisely the t<p satisfying f(a+t*p^k)=0 modulo p^(k+1)",
      "expansion_sha256": "b50d62cd193fb13107f093804c5f18ab270700303dfce4356d47eee62f9081c6",
      "meaning": "The exact possibly empty list of one-step root lifts.",
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      "name": "AllRootLifts",
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      "authority": "blueprint-vocabulary-only",
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        "SignedZeroWindow"
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      "expansion": "∃ dst_positive_code_bottomlayer. ∃ dst_positive_scale_bottomlayer. ∃ dst_negative_code_bottomlayer. ∃ dst_negative_scale_bottomlayer. ∃ dst_positive_bottomlayer. ∃ dst_negative_bottomlayer. MatrixMinorFourCode(F,dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer) ∧ (BetaAt(dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,i,dst_positive_bottomlayer) ∧ (BetaAt(dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer,i,dst_negative_bottomlayer) ∧ SignedBalance(z,dst_positive_bottomlayer,dst_negative_bottomlayer)))",
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      "expansion": "∃ dst_positive_code_bottomlayer. ∃ dst_positive_scale_bottomlayer. ∃ dst_negative_code_bottomlayer. ∃ dst_negative_scale_bottomlayer. MatrixMinorFourCode(F,dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer) ∧ (∀ x. Le(x,N) → ∃ y. ∃ z. ∃ n. BetaAt(dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,x,y) ∧ (BetaAt(dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer,x,z) ∧ SignedBalance(n,y,z)))",
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      "meaning": "A complete beta-coded binary digit prefix evaluating exactly to the supplied exponent.",
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        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "CRTPrefixGcdCongruences",
        "blueprint_parameters": [
          "b",
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          "l",
          "m",
          "u",
          "v"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "09bdc412032adc85c39a82d9b4605417dd02842bac8653045c7266ddac7553e0",
        "reviewed_id": "ND0076",
        "reviewed_name": "CRTPrefixGcdCongruences",
        "reviewed_parameters": [
          "b",
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          "l",
          "m",
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          "v"
        ],
        "route": "generalized-crt"
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      "topological_layer": 2,
      "transitive_dependencies": [
        "BetaAt",
        "Dvd",
        "IsGCD",
        "Lt",
        "ModEq"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Choose"
      ],
      "dependents": [],
      "expansion": "Choose(n + n,n,z)",
      "expansion_sha256": "e8a8da18a680e3de9355ed220136a54992e41b8cf7011df61c4934e0c47ca121",
      "meaning": "z is the central binomial coefficient Choose(2n,n).",
      "milestone_users": [
        "G027"
      ],
      "name": "CentralBinom",
      "parameters": [
        "n",
        "z"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "CentralBinom",
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "69b2ecb2eb05f496c0a91d739bfd19c9a4558b1c96cd86e319a16ab714a9ca2c",
        "reviewed_id": "PD0042",
        "reviewed_name": "CentralBinom",
        "reviewed_parameters": [
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        "route": "bertrand-postulate"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "Lt"
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      "transitive_dependents": []
    },
    {
      "arity": 8,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "ConvergentMatrixCode"
      ],
      "dependents": [
        "ConvergentMatrixTrace"
      ],
      "expansion": "∃ cfc_state_prioritylayer. ConvergentMatrixCode(s,u,U,v,V,cfc_state_prioritylayer) ∧ BetaAt(h,e,j,cfc_state_prioritylayer)",
      "expansion_sha256": "883692843e10d012836bb1cbfec16df660cd3233210c6a9e74b83e9831fb784f",
      "meaning": "A real beta history entry at j contains the actual coded quotient suffix and matrix state.",
      "milestone_users": [],
      "name": "ConvergentMatrixAt",
      "parameters": [
        "h",
        "e",
        "j",
        "s",
        "u",
        "U",
        "v",
        "V"
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      "reviewed_incompatibility": null,
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_id": "ND0203",
        "reviewed_name": "ConvergentMatrixAt",
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          "j",
          "s",
          "u",
          "U",
          "v",
          "V"
        ],
        "route": "best-approximation"
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      "topological_layer": 2,
      "transitive_dependencies": [
        "BetaAt",
        "ConvergentMatrixCode",
        "NaturalPair"
      ],
      "transitive_dependents": [
        "Convergent",
        "ConvergentMatrixTrace"
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    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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        "CornacchiaStateInvariant",
        "DirichletCoprimeProductData",
        "EuclidParameters",
        "EuclidParametrization",
        "JacobiBit",
        "MultiplicativePrefix",
        "PrimitiveFermatFourCounterexample",
        "PrimitivePythagorean",
        "SimpleHornerRoot",
        "UnitBitPrefix",
        "UnitProductFactor",
        "UnitScaledPrefix"
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      "expansion": "Gcd(a,b,1)",
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      "meaning": "Relative primality.",
      "milestone_users": [
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        "T14",
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        "G003",
        "G008",
        "G013",
        "G014",
        "G028",
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        "G045",
        "G095",
        "G107",
        "G108",
        "G109"
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      "name": "Coprime",
      "parameters": [
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "reviewed_expansion_sha256": "9309813a1797d5b48ddd1596997e568cefb9260ed22f0486c4675d6a70b58f8b",
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        "route": "quadratic-reciprocity"
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      "topological_layer": 2,
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      ],
      "transitive_dependents": [
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        "EuclidParametrization",
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        "MultiplicativePrefix",
        "Phi",
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        "PrimitivePythagorean",
        "PrimitiveRoot",
        "PrimitiveTriple",
        "SimpleHornerRoot",
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        "UnitCount",
        "UnitProductFactor",
        "UnitProductPrefix",
        "UnitScaledPrefix"
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    },
    {
      "arity": 2,
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        "Lt",
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      ],
      "dependents": [
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        "CornacchiaTrace"
      ],
      "expansion": "Prime(p) ∧ (¬z = 0 ∧ (Lt(z,p) ∧ Dvd(p,z · z + 1)))",
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      "meaning": "A prime p and an actual nonzero root z<p of z²+1 divisible by p.",
      "milestone_users": [
        "G107"
      ],
      "name": "CornacchiaRoot",
      "parameters": [
        "p",
        "z"
      ],
      "reviewed_incompatibility": null,
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        "blueprint_name": "CornacchiaRoot",
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        "reviewed_id": "ND0097",
        "reviewed_name": "CornacchiaRoot",
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        "route": "cornacchia"
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      "transitive_dependents": [
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        "CornacchiaTrace"
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    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt"
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      "dependents": [
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      ],
      "expansion": "∃ cor_a_secondwave. ∃ cor_r_secondwave. ∃ cor_u_secondwave. ∃ cor_t_secondwave. ∃ cor_q_secondwave. ∃ cor_next_a_secondwave. ∃ cor_next_r_secondwave. ∃ cor_next_u_secondwave. ∃ cor_next_t_secondwave. ∃ cor_next_q_secondwave. CornacchiaStateAt(h,e,S i,cor_a_secondwave,cor_r_secondwave,cor_u_secondwave,cor_t_secondwave,cor_q_secondwave) ∧ (CornacchiaStateAt(h,e,i,cor_next_a_secondwave,cor_next_r_secondwave,cor_next_u_secondwave,cor_next_t_secondwave,cor_next_q_secondwave) ∧ (cor_next_a_secondwave = cor_r_secondwave ∧ (cor_next_u_secondwave = cor_t_secondwave ∧ (cor_a_secondwave = cor_r_secondwave · cor_q_secondwave + cor_next_r_secondwave ∧ (Lt(cor_next_r_secondwave,cor_r_secondwave) ∧ (cor_next_t_secondwave = cor_q_secondwave · cor_t_secondwave + cor_u_secondwave ∧ Lt(p,cor_r_secondwave · cor_r_secondwave)))))))",
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      "meaning": "One actual quotient/remainder and coefficient update, with strict decrease and the pre-stopping square guard.",
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      "name": "CornacchiaTransitionAt",
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        "reviewed_name": "CornacchiaTransitionAt",
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        "route": "cornacchia"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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    },
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      "dependencies": [
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      ],
      "dependents": [],
      "expansion": "∀ dvi_index_lowercontinuation. Lt(dvi_index_lowercontinuation,l) → ∃ x. BetaAt(b,c,dvi_index_lowercontinuation,x) ∧ DivisorComplement(n,dvi_index_lowercontinuation,x)",
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      "meaning": "An actual beta prefix records complementary-divisor outputs at every i<l. For n>0 such prefixes exist at every length; the prefix of length S n is proved a permutation.",
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      "name": "DivisorComplementPrefix",
      "parameters": [
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        "reviewed_name": "DivisorComplementPrefix",
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        "route": "divisor-involutions"
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    {
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      "dependencies": [
        "Dvd",
        "PrimeFactorToggle"
      ],
      "dependents": [
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      "expansion": "¬d = 0 ∧ (Dvd(d,n) ∧ PrimeFactorToggle(p,d,e)) ∨ (d = 0 ∨ ¬Dvd(d,n)) ∧ e = d",
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      "meaning": "Apply the actual prime-factor toggle at positive divisors of n and fix zero and nondivisors. Closure in the divisor set and involutivity are proved under Prime(p), n>0 and Dvd(p,n).",
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      "name": "DivisorPrimeToggle",
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        "route": "mobius-divisor-cancellation"
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      "dependencies": [
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      ],
      "dependents": [],
      "expansion": "Prime(p),r>0,Curve(E,Fp), and N counts every affine point over F_(p^r) plus infinity",
      "expansion_sha256": "34be9e645c4b5b6e09b21ebc51bf26d26b2b745c91a8128f4fde333140d5800e",
      "meaning": "Point count over a finite extension.",
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      "name": "ECCount",
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      "dependencies": [
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      ],
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      "expansion": "∃q h s. ContinuedFractionTrace(a,b,q,h,s,k) ∧ EuclideanStateAt(h,s,0,g,0,0) ∧ Gcd(a,b,g)",
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      "meaning": "A complete actual Euclidean history whose terminal zero-remainder state is exactly its certified gcd output.",
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      "name": "EuclideanAnchoredExecution",
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        "route": "euclidean-gcd-transport"
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        "EuclideanStateAt",
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      "dependents": [],
      "expansion": "∃s h c k. ContinuedFractionTrace(a,b,s,h,c,k) ∧ Le(k,B)",
      "expansion_sha256": "341ad0706793998d705c1fbc5673007076029e091ed1349f9e9341b81e825cf1",
      "meaning": "An actual complete beta-coded Euclidean trace with a witnessed upper bound on its transition count.",
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      "name": "EuclideanBoundedTrace",
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        "route": "euclidean-logarithmic-bound"
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      "dependents": [],
      "expansion": "∃s u v. ContinuedFractionTrace(a,b,s,u,v,k) ∧ Gcd(a,b,g)",
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      "meaning": "A complete beta-coded Euclidean history together with an independently certified relational gcd; terminal-state identification is not asserted.",
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      "name": "EuclideanExecution",
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        "route": "euclidean-complexity"
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      "expansion": "Prime(p) ∧ (¬e = 0 ∧ (∃ x. ∃ y. ∃ z. p = S x ∧ (e = S y ∧ (Pow(p,y,z) ∧ c = z · x))))",
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      "meaning": "Complete finite prime-power field presentation.",
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      "meaning": "A nonempty canonical coefficient prefix has actual leading coefficient natural 1. Its length is still a representation annotation, not a degree definition; the empty zero polynomial is excluded. Natural field one is not signed code 2, and primality is not included in this graph.",
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      "expansion_sha256": "bcad50a2f7662fca0524e441873d062c532d98c825f8ff735225bb2b756ac701",
      "meaning": "The output consists of all and only the actual modular sums, with genuine operand witnesses for each output member.",
      "milestone_users": [
        "G051"
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      "name": "ModularSetSum",
      "parameters": [
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        "c",
        "d",
        "e",
        "u",
        "v",
        "p"
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "ModularSetSum",
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        "reviewed_id": "ND0134",
        "reviewed_name": "ModularSetSum",
        "reviewed_parameters": [
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          "d",
          "e",
          "u",
          "v",
          "p"
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        "route": "cauchy-davenport"
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      "transitive_dependencies": [
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        "ModEq",
        "ModularSetMember"
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      "transitive_dependents": []
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    {
      "arity": 6,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "Lt",
        "ModEq",
        "ModularSetMember"
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      "dependents": [],
      "expansion": "ModularSetMember(b,c,p,a) ∧ (Lt(r,p) ∧ (ModEq(p,a + d,r) ∧ ¬BetaAt(b,c,r,1)))",
      "expansion_sha256": "297b6591641eea4ed29778139e83b5c960a091ac9c5249a28513938b79c03e5b",
      "meaning": "An actual in-set residue a and canonical shifted residue r≡a+d outside the set witness a translation boundary.",
      "milestone_users": [
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      "name": "ModularTranslationBoundary",
      "parameters": [
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        "p",
        "d",
        "a",
        "r"
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      "reviewed_incompatibility": null,
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        "reviewed_name": "ModularTranslationBoundary",
        "reviewed_parameters": [
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          "p",
          "d",
          "a",
          "r"
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        "route": "cauchy-davenport"
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      "transitive_dependencies": [
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        "ModEq",
        "ModularSetMember"
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      "transitive_dependents": []
    },
    {
      "arity": 7,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "Choose",
        "Lt"
      ],
      "dependents": [
        "Multinomial"
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      "expansion": "∀ mkm_index_secondwave. Lt(mkm_index_secondwave,l) → ∃ x. ∃ y. ∃ z. BetaAt(b,c,mkm_index_secondwave,x) ∧ (BetaAt(sb,sc,mkm_index_secondwave,y) ∧ (Choose(y + x,y,z) ∧ BetaAt(cb,cc,mkm_index_secondwave,z)))",
      "expansion_sha256": "353b7d34b201bf2325a0a5be4b88a63e2f89c38f78a805a9d291f901e4326ff2",
      "meaning": "The actual factor at each position is Choose(previous total + next part, previous total).",
      "milestone_users": [
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      ],
      "name": "MultinomialBinomialPrefix",
      "parameters": [
        "b",
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        "sb",
        "sc",
        "cb",
        "cc",
        "l"
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      "reviewed_incompatibility": null,
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        "blueprint_name": "MultinomialBinomialPrefix",
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          "cb",
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        "reviewed_id": "ND0088",
        "reviewed_name": "MultinomialBinomialPrefix",
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          "sb",
          "sc",
          "cb",
          "cc",
          "l"
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        "route": "multinomial-kummer"
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      "topological_layer": 2,
      "transitive_dependencies": [
        "BetaAt",
        "Choose",
        "Le",
        "Lt"
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      "transitive_dependents": [
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    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Le",
        "Lt",
        "Prime"
      ],
      "dependents": [
        "InitialPrimeChain"
      ],
      "expansion": "Prime(p) ∧ (Lt(a,p) ∧ (∀ x. Prime(x) → Lt(a,x) → Le(p,x)))",
      "expansion_sha256": "6951135826c2ed6a3a3b380db8546e767b894a50bcbf87a69c12e4e1b5de52a9",
      "meaning": "The actual least prime strictly above a. Global minimality excludes a sparse subsequence of primes.",
      "milestone_users": [],
      "name": "NextPrime",
      "parameters": [
        "a",
        "p"
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      "reviewed_incompatibility": null,
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        "blueprint_name": "NextPrime",
        "blueprint_parameters": [
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "964367d85994baf9339758cc05f0d2e10ee3acee39aba4c569aeebfe0c510b50",
        "reviewed_id": "ND0152",
        "reviewed_name": "NextPrime",
        "reviewed_parameters": [
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        ],
        "route": "prime-enumeration"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "Le",
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      "transitive_dependents": [
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    },
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "InjectivePrefix",
        "SurjectivePrefix"
      ],
      "dependents": [
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        "PrimeFactorListPermutation"
      ],
      "expansion": "BoundedPrefix(b,c,l) ∧ (InjectivePrefix(b,c,l) ∧ SurjectivePrefix(b,c,l))",
      "expansion_sha256": "b4d81d2605b128f4d9ff4b2dface2b4169b61bf018c00395ce54ac5ade31dff4",
      "meaning": "An actual beta-coded bijection of the finite index interval [0,l), including all bounds, injectivity, and surjectivity.",
      "milestone_users": [],
      "name": "PermutationPrefix",
      "parameters": [
        "b",
        "c",
        "l"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "PermutationPrefix",
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        "reviewed_expansion_sha256": "4145090a616c423da718870c305d9d2c207fc0111a74c2e543158ef031c699fb",
        "reviewed_id": "ND0148",
        "reviewed_name": "PermutationPrefix",
        "reviewed_parameters": [
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        "route": "arithmetic-foundations"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "BoundedPrefix",
        "InjectivePrefix",
        "Lt",
        "SurjectivePrefix"
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      "transitive_dependents": [
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        "GMatchedFactors",
        "PrimeFactorListPermutation"
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    },
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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      "expansion": "∃ pfc_complement_lowercontinuation. ∃ pfc_left_lowercontinuation. ∃ pfc_right_lowercontinuation. j + pfc_complement_lowercontinuation = i ∧ (BetaZeroExtend(ab,ac,L,j,pfc_left_lowercontinuation) ∧ (BetaZeroExtend(bb,bc,M,pfc_complement_lowercontinuation,pfc_right_lowercontinuation) ∧ t = pfc_left_lowercontinuation · pfc_right_lowercontinuation))",
      "expansion_sha256": "476047ffc3b9c731ecb1e3853948c7b37c656de7fe880af1058500603bd93173",
      "meaning": "Witness k with j+k=i and multiply the two actual zero-extended coefficients. These are natural products in a highest-degree-first antidiagonal, before reduction modulo the field prime.",
      "milestone_users": [],
      "name": "PolynomialDiagonalTerm",
      "parameters": [
        "ab",
        "ac",
        "L",
        "bb",
        "bc",
        "M",
        "i",
        "j",
        "t"
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      "reviewed_incompatibility": null,
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        "blueprint_name": "PolynomialDiagonalTerm",
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        "reviewed_expansion_sha256": "7fd028e416918483a8f5913be6490d89a8004958fdd30ef87030107f77f9e7ea",
        "reviewed_id": "ND0292",
        "reviewed_name": "PolynomialDiagonalTerm",
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          "i",
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        "route": "polynomial-products"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "BetaZeroExtend",
        "Le",
        "Lt"
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      "transitive_dependents": [
        "FpConvolutionCoefficient",
        "FpConvolutionPrefix",
        "FpPolyProduct",
        "PolynomialDiagonalPrefix"
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    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "Lt",
        "Prime"
      ],
      "dependents": [],
      "expansion": "∀ pc_index_secondwave. Lt(pc_index_secondwave,l) → ∃ x. BetaAt(b,c,pc_index_secondwave,x) ∧ (Prime(S pc_index_secondwave) ∧ x = 1 ∨ ¬Prime(S pc_index_secondwave) ∧ x = 0)",
      "expansion_sha256": "24e070f80dc5bc83597a3eb64f1d17be5ce6033ca39a40c88709f8a904cf0f76",
      "meaning": "At each index i<l the actual bit is one exactly when S i is prime, and otherwise zero.",
      "milestone_users": [
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      ],
      "name": "PrimeBitPrefix",
      "parameters": [
        "b",
        "c",
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "PrimeBitPrefix",
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        "reviewed_expansion_sha256": "ee8d088338a057d2b9c5835c8ea2cf40c47cc6cffc45a1492f61c7b83e9050b8",
        "reviewed_id": "ND0094",
        "reviewed_name": "PrimeBitPrefix",
        "reviewed_parameters": [
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        "route": "prime-count-chebyshev"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "Dvd",
        "Lt",
        "Prime"
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      "transitive_dependents": []
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt",
        "Prime"
      ],
      "dependents": [
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      ],
      "expansion": "∀ pvs_divisor_prioritylayer. Prime(pvs_divisor_prioritylayer) → Dvd(pvs_divisor_prioritylayer,n) → ∃ x. Lt(x,l) ∧ BetaAt(pb,pc,x,pvs_divisor_prioritylayer)",
      "expansion_sha256": "3229bdddf4c1f89499610776792031e51c75df134ebcb62c7d459d7a85778f0a",
      "meaning": "Every actual prime divisor of n occurs at a witnessed index in this prime prefix; no prime divisor may be omitted.",
      "milestone_users": [],
      "name": "PrimeDivisorSupport",
      "parameters": [
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        "pb",
        "pc",
        "l"
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "PrimeDivisorSupport",
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        "reviewed_id": "ND0180",
        "reviewed_name": "PrimeDivisorSupport",
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        "route": "prime-valuation-support"
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    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      ],
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      "expansion": "Prime(p) ∧ Mod4Three(p) ∧ Dvd(p,n)",
      "expansion_sha256": "1983c6792a16f992562c607be6aee673cba0e5afb6c0845a90bfd7e13f8972df",
      "meaning": "A genuine prime divisor in the exact residue class three modulo four.",
      "milestone_users": [
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      "name": "PrimeThreeModFourDivisor",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "blueprint_name": "PrimeThreeModFourDivisor",
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        "reviewed_id": "ND0044",
        "reviewed_name": "PrimeThreeModFourDivisor",
        "reviewed_parameters": [
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        "route": "primes-three-mod-four"
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    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "expansion": "w witnesses m=2, m=4, m=p^k, or m=2*p^k for an odd Prime p and k>0",
      "expansion_sha256": "f0457dcf3d74960bb77922eaba76cd77d8a181acd331dbccb328a07a57fae2f4",
      "meaning": "Exact modulus classification with primitive roots.",
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      "name": "PrimitiveRootModulus",
      "parameters": [
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      "reviewed_incompatibility": null,
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      "topological_layer": 2,
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      "dependencies": [
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      "dependents": [],
      "expansion": "∃ bpr_code_bertrand_defined_primorial. ∃ bpr_scale_bertrand_defined_primorial. (∀ x. Lt(x,n) → ∃ y. BetaAt(bpr_code_bertrand_defined_primorial,bpr_scale_bertrand_defined_primorial,x,y) ∧ (Prime(S x) ∧ y = S x ∨ ¬Prime(S x) ∧ y = 1)) ∧ Product(bpr_code_bertrand_defined_primorial,bpr_scale_bertrand_defined_primorial,n,z)",
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      "meaning": "z is the finite product of the primes at most n.",
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      "parameters": [
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        "blueprint_name": "Primorial",
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        "reviewed_id": "PD0043",
        "reviewed_name": "Primorial",
        "reviewed_parameters": [
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        "route": "bertrand-postulate"
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    {
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      "expansion": "Prime(p) ∧ p>2 ∧ ¬Dvd(p,a) ∧ s<2 ∧ (s=0 ↔ ∃ x<p. Mod(x*x,a,p))",
      "expansion_sha256": "3fc5aaad09eda6e32a1cfe8ca2d908a73cbf5bd91eafcdb4f1b3d6271e3d0fb6",
      "meaning": "Quadratic-character sign bit.",
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        "A03",
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        "G044"
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      "name": "QuadBit",
      "parameters": [
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      "topological_layer": 2,
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      "dependencies": [
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      "dependents": [],
      "expansion": "UnitResidue(m,a) ∧ ModEq(m,a · a,t)",
      "expansion_sha256": "1949667af9f87dcf4b1e9d637e9858d4c0828bdad202774555b93b23d1a3e597",
      "meaning": "a is a bounded unit whose square is t modulo m.",
      "milestone_users": [],
      "name": "ScaledFixedPoint",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "reviewed_name": "ScaledFixedPoint",
        "reviewed_parameters": [
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        "route": "quadratic-reciprocity"
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    {
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      "dependencies": [
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        "m",
        "t",
        "a",
        "b"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "ScaledInverse",
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        "reviewed_id": "PD0033",
        "reviewed_name": "ScaledInverse",
        "reviewed_parameters": [
          "m",
          "t",
          "a",
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        ],
        "route": "quadratic-reciprocity"
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      "topological_layer": 2,
      "transitive_dependencies": [
        "Lt",
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      "transitive_dependents": [
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    },
    {
      "arity": 13,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Beta",
        "Lt",
        "SignedAlternatingCofactorTerm"
      ],
      "dependents": [
        "SignedAlternatingCofactorFold"
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      "expansion": "∀i ap an bp bn p n. Lt(i,l) → Beta(ab,ac,i,ap) → Beta(db,dc,i,an) → Beta(eb,ec,i,bp) → Beta(fb,fc,i,bn) → Beta(ub,uc,i,p) → Beta(vb,vc,i,n) → SignedAlternatingCofactorTerm(ap,an,bp,bn,i,p,n)",
      "expansion_sha256": "f28460440de75e1871dc2a840db9f85c8e9e180864c03a3a6f9c26d78779d4af",
      "meaning": "Two complete beta-coded output streams containing every actual parity-correct signed cofactor-product component.",
      "milestone_users": [
        "T13"
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      "name": "SignedAlternatingProductPrefix",
      "parameters": [
        "ab",
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        "dc",
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      "reviewed_incompatibility": null,
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        "reviewed_expansion_sha256": "76fafd74f57de662747a4ce9020a1973c2452c087358d0a4c238c17d45163b2a",
        "reviewed_id": "ND0062",
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          "ab",
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          "fc",
          "ub",
          "uc",
          "vb",
          "vc",
          "l"
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        "route": "matrix-cofactor-expansion"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "Odd",
        "SignedAlternatingCofactorTerm"
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      "transitive_dependents": [
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        "AllSignedMinorsZero",
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        "PositiveDeterminantMatrixData",
        "RectangularMatrixRank",
        "SignedAlternatingCofactorFold",
        "SignedDeterminantHistory",
        "SignedDeterminantLocalStep",
        "SignedEvaluatedCofactors",
        "SignedFirstRowCofactorFold",
        "SignedRecursiveDeterminant",
        "SignedSelectedDeterminant"
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    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "SignedFloor"
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      "dependents": [],
      "expansion": "∃ sif_positive_lowerlayer. ∃ sif_negative_lowerlayer. ∃ sif_quotient_positive_lowerlayer. ∃ sif_quotient_negative_lowerlayer. SignedDecode(a,sif_positive_lowerlayer,sif_negative_lowerlayer) ∧ (SignedDecode(q,sif_quotient_positive_lowerlayer,sif_quotient_negative_lowerlayer) ∧ SignedFloor(sif_positive_lowerlayer,sif_negative_lowerlayer,m,sif_quotient_positive_lowerlayer,sif_quotient_negative_lowerlayer,r))",
      "expansion_sha256": "8996f90c1f9aa69ec459eb5dd394d42f0afdcfcbbc4f00f8bca5352fa10f4f64",
      "meaning": "Actual canonical signed input and quotient codes satisfy the very same floor equation with remainder r<m.",
      "milestone_users": [],
      "name": "SignedCodeFloor",
      "parameters": [
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        "q",
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      "reviewed_incompatibility": null,
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        "blueprint_name": "SignedCodeFloor",
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        "reviewed_name": "SignedCodeFloor",
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        "route": "gaussian-integers"
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        "SignedFloor"
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    {
      "arity": 11,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "∃pp nn pn np. DotProduct(ab,ac,eb,ec,l,pp) ∧ DotProduct(db,dc,fb,fc,l,nn) ∧ DotProduct(ab,ac,fb,fc,l,pn) ∧ DotProduct(db,dc,eb,ec,l,np) ∧ p=pp+nn ∧ n=pn+np",
      "expansion_sha256": "b2517e88d9ca873fd13a2fc6c7fe1284b4f409333b265cb10f35f1c3a8924607",
      "meaning": "The exact positive and negative dot-product components of two arbitrary finite signed vectors.",
      "milestone_users": [],
      "name": "SignedDotProduct",
      "parameters": [
        "ab",
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        "db",
        "dc",
        "eb",
        "ec",
        "fb",
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        "l",
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        "blueprint_name": "SignedDotProduct",
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          "fb",
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        "reviewed_expansion_sha256": "2e16777bbacfe38439d7aed05af2fe3ab87c4c711cf4c66f42066c9ad2d5bd03",
        "reviewed_id": "ND0016",
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        "route": "matrix-coded-products"
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "ModEq"
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      "dependents": [
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      ],
      "expansion": "∃ sph_positive_secondwave. ∃ sph_negative_secondwave. Horner(pb,pc,a,l,sph_positive_secondwave) ∧ (Horner(nb,nc,a,l,sph_negative_secondwave) ∧ ModEq(m,sph_positive_secondwave,sph_negative_secondwave))",
      "expansion_sha256": "b51ddc1dd7ab151e9909cecaecb4429a015310f5b3f8f0716f5a4ec547311931",
      "meaning": "The actual positive and negative polynomial values agree modulo m.",
      "milestone_users": [
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      "name": "SignedHornerRoot",
      "parameters": [
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        "pc",
        "nb",
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        "a",
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        "m"
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        "blueprint_name": "SignedHornerRoot",
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        "reviewed_id": "ND0084",
        "reviewed_name": "SignedHornerRoot",
        "reviewed_parameters": [
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        "route": "hensel-lifting"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaSum",
        "MatrixMinorFourCode",
        "SignedBalance"
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      "dependents": [
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        "DivisorSum",
        "SignedRectangularSum",
        "SignedSliceSum",
        "SignedWeightedSum"
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      "expansion": "∃ dst_positive_code_bottomlayer. ∃ dst_positive_scale_bottomlayer. ∃ dst_negative_code_bottomlayer. ∃ dst_negative_scale_bottomlayer. ∃ dst_positive_sum_bottomlayer. ∃ dst_negative_sum_bottomlayer. MatrixMinorFourCode(F,dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer) ∧ (BetaSum(dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,l,dst_positive_sum_bottomlayer) ∧ (BetaSum(dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer,l,dst_negative_sum_bottomlayer) ∧ SignedBalance(z,dst_positive_sum_bottomlayer,dst_negative_sum_bottomlayer)))",
      "expansion_sha256": "89b8f4ebf8bd5121970bf1a27b8195fd52831db673b420cc47dd29d6e2d15215",
      "meaning": "The signed balance of two actual natural finite sums, at exactly the indices 0<=i<l. Existence, uniqueness and representation independence are proved separately.",
      "milestone_users": [],
      "name": "SignedPrefixSum",
      "parameters": [
        "F",
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        "blueprint_name": "SignedPrefixSum",
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        "reviewed_id": "ND0253",
        "reviewed_name": "SignedPrefixSum",
        "reviewed_parameters": [
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        "route": "signed-arithmetic"
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      "topological_layer": 2,
      "transitive_dependencies": [
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        "SignedDecode"
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      "transitive_dependents": [
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        "DivisorTransform",
        "SignedRectangularSum",
        "SignedSliceSum",
        "SignedWeightedSum"
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    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "Prime(p),k>0,f(a)=0 modulo p^k,f′(a) is a unit modulo p, b=a modulo p^k, and f(b)=0 modulo p^(k+1)",
      "expansion_sha256": "728166a7e1e670130562bb9ec26ee5b4013a076694b2f200a577fd7489100a09",
      "meaning": "A simple Hensel lift.",
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      "name": "SimpleLift",
      "parameters": [
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      "reviewed_incompatibility": null,
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      "topological_layer": 2,
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    {
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      "dependencies": [
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        "Le",
        "Prime"
      ],
      "dependents": [
        "NaturalSquarefreeDecomposition"
      ],
      "expansion": "¬n = 0 ∧ (∀ x. Prime(x) → Le(x,n) → ¬Dvd(x · x,n))",
      "expansion_sha256": "e6f50eea443e5df90201a0d07cf686d0450712bf3a9e48fb9341c196a61d26cc",
      "meaning": "Positive n with no squared prime divisor p² for any prime p≤n. The bounded condition is proved to exclude all squared prime divisors.",
      "milestone_users": [
        "G010"
      ],
      "name": "Squarefree",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "blueprint_name": "Squarefree",
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        "reviewed_id": "ND0188",
        "reviewed_name": "Squarefree",
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        "route": "squarefree-kernels"
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "Prime(p),k>0,a<p,w<p^k,Mod(w,a,p),and Mod(w^p,w,p^k)",
      "expansion_sha256": "36cb47ccea5b760a3b0a799d842226aef2e0f72e9247caefe6a2c5bd2105ac38",
      "meaning": "Finite-precision Teichmüller representative.",
      "milestone_users": [
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      "name": "TeichLift",
      "parameters": [
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      "reviewed_incompatibility": null,
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      "topological_layer": 2,
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      "dependencies": [
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      ],
      "dependents": [],
      "expansion": "∀ eu_index_bottomlayer. Lt(eu_index_bottomlayer,l) → ∃ x. BetaAt(b,c,eu_index_bottomlayer,x) ∧ CanonicalModularResidue(m,a · eu_index_bottomlayer,x)",
      "expansion_sha256": "3afb23cb5b6d8bfd358fc71083cd837588d39c2af1c7f8f050701ccd561d1328",
      "meaning": "At every index i<l, the actual beta entry is the canonical residue of a*i. A bijection is constructed by theorem, not assumed in this graph.",
      "milestone_users": [],
      "name": "UnitMultiplierPrefix",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "route": "euler-units"
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      "dependencies": [
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      "dependents": [
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      "expansion": "Prime(p) ∧ n>0 ∧ ∃ u. n=p^e*u ∧ ¬Dvd(p,u)",
      "expansion_sha256": "1cd97bb90f66029a3f7f1496552af96c09ac84ccb1b86230078b8ad70a57735f",
      "meaning": "p-adic valuation only for a positive natural.",
      "milestone_users": [
        "G023",
        "G038",
        "G039",
        "G040"
      ],
      "name": "Val",
      "parameters": [
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      "topological_layer": 2,
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    },
    {
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      "dependencies": [
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      "dependents": [],
      "expansion": "Prime(p),k>0,0<d<M, f is a distinguished HA-total coefficient-function code with a supplied precision modulus, and w verifies the canonical complete-ring factorization through the requested output precision; no uniqueness is inferred from naive independent truncations",
      "expansion_sha256": "b8c7f620dc35abe1139acfcbe81439e8dabe5aeb48736755a58afc220246956a",
      "meaning": "Normalized preparation from sufficient COUPLED finite source precision.",
      "milestone_users": [
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      "name": "WeierstrassCertificate",
      "parameters": [
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      "dependencies": [
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      "dependents": [
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        "ZPairAdd"
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      "expansion": "∃ ge_representation_real_code_lowerlayer. ∃ ge_representation_imaginary_code_lowerlayer. z = (ge_representation_real_code_lowerlayer + ge_representation_imaginary_code_lowerlayer) · S (ge_representation_real_code_lowerlayer + ge_representation_imaginary_code_lowerlayer) + (ge_representation_imaginary_code_lowerlayer + ge_representation_imaginary_code_lowerlayer) ∧ (SignedBalance(ge_representation_real_code_lowerlayer,ap,an) ∧ SignedBalance(ge_representation_imaginary_code_lowerlayer,bp,bn))",
      "expansion_sha256": "9bfca2534cc23e0911967e586a7001554ee8c17b9cb39c97cb15d9fb0e5f2761",
      "meaning": "The shared pair code represents the two supplied signed differences, with arbitrary nonnormalized representatives allowed.",
      "milestone_users": [],
      "name": "ZPairRep",
      "parameters": [
        "z",
        "ap",
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        "route": "gaussian-integers"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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        "GAssociate",
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        "GDvd",
        "GEuclideanDivision",
        "GFactorAssociateMatching",
        "GFactorPermutation",
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        "GIrreducibleFactorization",
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        "GProductStep",
        "GProductSteps",
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ZPairDecode"
      ],
      "dependents": [
        "GEuclideanDivision",
        "GIrreducible",
        "GPrime"
      ],
      "expansion": "∃ ge_real_positive_lowerlayer. ∃ ge_real_negative_lowerlayer. ∃ ge_imaginary_positive_lowerlayer. ∃ ge_imaginary_negative_lowerlayer. ZPairDecode(z,ge_real_positive_lowerlayer,ge_real_negative_lowerlayer,ge_imaginary_positive_lowerlayer,ge_imaginary_negative_lowerlayer)",
      "expansion_sha256": "067f1b90efdf012c321d2f80f08e02a56be350411bbe53591a8506b607cfc3e7",
      "meaning": "The natural z actually encodes a pair of signed integers; not every natural is assumed to be a valid pair code.",
      "milestone_users": [
        "G081",
        "G082",
        "G084"
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      "name": "ZPairValid",
      "parameters": [
        "z"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "ZPairValid",
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        ],
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        "reviewed_id": "ND0160",
        "reviewed_name": "ZPairValid",
        "reviewed_parameters": [
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        "route": "gaussian-integers"
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      "topological_layer": 2,
      "transitive_dependencies": [
        "SignedDecode",
        "ZPairDecode"
      ],
      "transitive_dependents": [
        "GAllIrreducible",
        "GAllPrime",
        "GEuclideanDivision",
        "GIrreducible",
        "GIrreducibleFactorization",
        "GPrime",
        "GPrimeFactorization"
      ]
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt",
        "ArithTable",
        "Lt",
        "SignedAdd"
      ],
      "dependents": [],
      "expansion": "ArithTable(l,F) ∧ (ArithTable(l,G) ∧ (ArithTable(l,H) ∧ (∀ x. Lt(x,l) → ∃ y. ∃ z. ∃ n. ArithAt(F,x,y) ∧ (ArithAt(G,x,z) ∧ (ArithAt(H,x,n) ∧ SignedAdd(y,z,n))))))",
      "expansion_sha256": "063b4822aeed265393dc8b09286223eb5f610d8f3a52d84142262204011b5cae",
      "meaning": "Three actual signed tables and witnessed SignedAdd entries at each i<l. The unused endpoint certified by ArithTable(l,...) is not included in the prefix sum.",
      "milestone_users": [],
      "name": "ArithAdd",
      "parameters": [
        "F",
        "G",
        "H",
        "l"
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        "reviewed_name": "ArithAdd",
        "reviewed_parameters": [
          "F",
          "G",
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        "route": "signed-weighted-sums"
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      "topological_layer": 3,
      "transitive_dependencies": [
        "ArithAt",
        "ArithTable",
        "BetaAt",
        "Le",
        "Lt",
        "MatrixMinorFourCode",
        "SignedAdd",
        "SignedBalance",
        "SignedDecode"
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      "transitive_dependents": []
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt",
        "ArithTable",
        "Lt",
        "SignedMul"
      ],
      "dependents": [
        "SignedWeightedSum"
      ],
      "expansion": "ArithTable(l,F) ∧ (ArithTable(l,G) ∧ (ArithTable(l,H) ∧ (∀ x. Lt(x,l) → ∃ y. ∃ z. ∃ n. ArithAt(F,x,y) ∧ (ArithAt(G,x,z) ∧ (ArithAt(H,x,n) ∧ SignedMul(y,z,n))))))",
      "expansion_sha256": "10c7683b92d5de33765010a06508991ee31d11975f2fbe0544e537c709c1916b",
      "meaning": "Three actual signed tables and witnessed SignedMul entries at each i<l; neither a finite-choice principle nor a product-of-sums identity is assumed.",
      "milestone_users": [],
      "name": "ArithMul",
      "parameters": [
        "F",
        "G",
        "H",
        "l"
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "ArithMul",
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        "reviewed_id": "ND0267",
        "reviewed_name": "ArithMul",
        "reviewed_parameters": [
          "F",
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        "route": "signed-weighted-sums"
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      "transitive_dependencies": [
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        "Le",
        "Lt",
        "MatrixMinorFourCode",
        "SignedBalance",
        "SignedDecode",
        "SignedMul"
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      "transitive_dependents": [
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    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt",
        "SignedNegate"
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      "dependents": [],
      "expansion": "∀ mdc_index_lowercontinuation. ∀ mdc_source_lowercontinuation. ∀ mdc_target_lowercontinuation. Lt(mdc_index_lowercontinuation,l) → ArithAt(F,mdc_index_lowercontinuation,mdc_source_lowercontinuation) → ArithAt(G,mdc_index_lowercontinuation,mdc_target_lowercontinuation) → SignedNegate(mdc_source_lowercontinuation,mdc_target_lowercontinuation)",
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      "meaning": "Every pair of actual represented signed values at the same i<l are opposite. Genuine table validity is a separate hypothesis; arbitrary codes and component streams need not agree.",
      "milestone_users": [],
      "name": "ArithNegate",
      "parameters": [
        "F",
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        "blueprint_name": "ArithNegate",
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        "reviewed_id": "ND0286",
        "reviewed_name": "ArithNegate",
        "reviewed_parameters": [
          "F",
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        ],
        "route": "mobius-divisor-cancellation"
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      "topological_layer": 3,
      "transitive_dependencies": [
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        "BetaAt",
        "Lt",
        "MatrixMinorFourCode",
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        "SignedDecode",
        "SignedNegate"
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    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Le"
      ],
      "dependents": [],
      "expansion": "∀ dm_index_lowertier. ∀ dm_first_value_lowertier. ∀ dm_second_value_lowertier. ¬dm_index_lowertier = 0 → Le(dm_index_lowertier,N) → ArithAt(F,dm_index_lowertier,dm_first_value_lowertier) → ArithAt(G,dm_index_lowertier,dm_second_value_lowertier) → dm_first_value_lowertier = dm_second_value_lowertier",
      "expansion_sha256": "211bed5ccc7ce562c0867b3c4bde7988f16b1d59d0f16abaf24ea33ccaaf20f1",
      "meaning": "Equality of represented values at precisely 0<d<=N. Values at zero are unrestricted, and raw codes or positive/negative representatives are not asserted equal.",
      "milestone_users": [
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        "G009"
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      "name": "ArithPositiveEqual",
      "parameters": [
        "F",
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        "blueprint_name": "ArithPositiveEqual",
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        "reviewed_id": "ND0276",
        "reviewed_name": "ArithPositiveEqual",
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        "route": "divisor-sums"
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      "topological_layer": 3,
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        "SignedBalance",
        "SignedDecode"
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      "transitive_dependents": []
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    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [],
      "expansion": "∀ dsr_index_bottomlayer. ∀ dsr_image_bottomlayer. ∀ dsr_value_bottomlayer. Lt(dsr_index_bottomlayer,l) → BetaAt(r,s,dsr_index_bottomlayer,dsr_image_bottomlayer) → ArithAt(F,dsr_image_bottomlayer,dsr_value_bottomlayer) → ArithAt(G,dsr_index_bottomlayer,dsr_value_bottomlayer)",
      "expansion_sha256": "355ae3be1350010c671e9c7519dcaa750938f8ae6d43794093bfe6683be15c96",
      "meaning": "Actual beta-map lookup pulls each source signed value into the target table below l. Neither permutation bijectivity nor any sum identity is assumed in this graph.",
      "milestone_users": [],
      "name": "ArithReindex",
      "parameters": [
        "F",
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        "reviewed_expansion_sha256": "e2def0a877caf9f0efafca96b0c3182f3fdc5da6a6f35cba577b58fa8b8627dd",
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        "reviewed_name": "ArithReindex",
        "reviewed_parameters": [
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        "route": "signed-arithmetic"
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      "transitive_dependencies": [
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        "Lt",
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        "SignedBalance",
        "SignedDecode"
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      "transitive_dependents": []
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt",
        "ArithTable",
        "Lt",
        "SignedMul"
      ],
      "dependents": [],
      "expansion": "ArithTable(l,F) ∧ (ArithTable(l,G) ∧ (∀ x. Lt(x,l) → ∃ y. ∃ z. ArithAt(F,x,y) ∧ (ArithAt(G,x,z) ∧ SignedMul(a,y,z))))",
      "expansion_sha256": "59d96c51456bb4b3dc0b13e04e6ff5ee005a4dd50bb1e3007b4c721cf080b208",
      "meaning": "Actual source and output tables with witnessed multiplication of every represented entry below l by the signed scalar a. Sum distributivity is a separate theorem.",
      "milestone_users": [],
      "name": "ArithScale",
      "parameters": [
        "a",
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        "G",
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      "reviewed_incompatibility": null,
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        "route": "signed-weighted-sums"
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      "topological_layer": 3,
      "transitive_dependencies": [
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    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt"
      ],
      "dependents": [
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      ],
      "expansion": "ArithTable(0,F) ∧ (ArithTable(l,G) ∧ (∀ x. Lt(x,l) → ∃ y. ArithAt(F,o + s · x,y) ∧ ArithAt(G,x,y)))",
      "expansion_sha256": "c900952296e34ac252daa354049f1f55098f9c9bc56d8ed4dda505789d68cc33",
      "meaning": "Actual signed tables with witnessed values G(i)=F(o+s*i) for i<l. The output is constructed by real beta-stream recoding; its separately certified endpoint is unused.",
      "milestone_users": [],
      "name": "ArithSlice",
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      "reviewed_incompatibility": null,
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        "route": "rectangular-sums"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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      "expansion": "∀ dst_index_bottomlayer. ∀ dst_first_bottomlayer. ∀ dst_second_bottomlayer. Lt(dst_index_bottomlayer,l) → ArithAt(F,dst_index_bottomlayer,dst_first_bottomlayer) → ArithAt(G,dst_index_bottomlayer,dst_second_bottomlayer) → dst_first_bottomlayer = dst_second_bottomlayer",
      "expansion_sha256": "ddb8c3cfa24fd0acb14e9927b9416e6e844667cf1fc9758d22733204ee8cb5ca",
      "meaning": "Pointwise equality of actual canonical signed lookups below l, not equality of table codes or their positive/negative components.",
      "milestone_users": [],
      "name": "ArithTableEqual",
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      "reviewed_incompatibility": null,
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        "reviewed_name": "ArithTableEqual",
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        "route": "signed-arithmetic"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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      "dependencies": [
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      "dependents": [],
      "expansion": "Beta(b,c,0,n) ∧ ∀i. Lt(i,k) → ∃u v. Beta(b,c,i,u) ∧ Beta(b,c,i+1,v) ∧ BertrandWindow(u,v)",
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      "meaning": "A beta-coded finite chain beginning at n with a strict Bertrand prime step at every bounded edge.",
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      "name": "BertrandChain",
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        "route": "bertrand-prime-chains"
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      "dependents": [],
      "expansion": "∀ mkm_index_secondwave. Lt(mkm_index_secondwave,l) → ∃ x. ∃ y. BetaAt(b,c,mkm_index_secondwave,x) ∧ (BetaAt(vb,vc,mkm_index_secondwave,y) ∧ BoundedPowerValuation(p,x,x,y))",
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      "expansion": "BitLen(e,ell) ∧ BinaryExponentDigitCode(e,ell,b,c)",
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        "reviewed_name": "BinaryCanonicalExponentDigitCode",
        "reviewed_parameters": [
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        "PowTwo"
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      "dependents": [
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      "expansion": "∃ mkm_lb_secondwave. ∃ mkm_lc_secondwave. ∃ mkm_rb_secondwave. ∃ mkm_rc_secondwave. ∃ mkm_tb_secondwave. ∃ mkm_tc_secondwave. ∃ mkm_cb_secondwave. ∃ mkm_cc_secondwave. PowerQuotPrefix(p,a,mkm_lb_secondwave,mkm_lc_secondwave,a + b) ∧ (PowerQuotPrefix(p,b,mkm_rb_secondwave,mkm_rc_secondwave,a + b) ∧ (PowerQuotPrefix(p,a + b,mkm_tb_secondwave,mkm_tc_secondwave,a + b) ∧ (BinaryAddCarryPrefix(mkm_lb_secondwave,mkm_lc_secondwave,mkm_rb_secondwave,mkm_rc_secondwave,mkm_tb_secondwave,mkm_tc_secondwave,mkm_cb_secondwave,mkm_cc_secondwave,a + b) ∧ BitCount(mkm_cb_secondwave,mkm_cc_secondwave,a + b,e))))",
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      "name": "BinaryColumnCarryCount",
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      "expansion": "∃e. Horner(d,s,2,n,e) ∧ BinaryModularPower(a,e,m,r)",
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      "expansion": "Beta(h,t,0,1) ∧ ∀i. Lt(i,n) → ∃b u v. Beta(d,s,i,b) ∧ Beta(h,t,i,u) ∧ Beta(h,t,i+1,v) ∧ BinaryModularStep(m,u,a,b,v)",
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      "expansion": "Lt(r,M) ∧ (ModEq(m,r,a) ∧ SignedHornerRoot(pb,pc,nb,nc,r,l,M))",
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        "reviewed_expansion_sha256": "59a5ed5327a7cb8d176b80f228db9b080d77a2414b50a6bbcbadd46e0cfaa989",
        "reviewed_id": "ND0099",
        "reviewed_name": "CornacchiaStateInvariant",
        "reviewed_parameters": [
          "p",
          "z",
          "a",
          "r",
          "u",
          "t"
        ],
        "route": "cornacchia"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "Coprime",
        "CornacchiaAlternatingCongruences",
        "CornacchiaRoot",
        "Dvd",
        "Gcd",
        "Lt",
        "ModEq",
        "Prime"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt",
        "Dvd",
        "SignedMul"
      ],
      "dependents": [
        "DirichletDivisorGridWitness",
        "DirichletPrefix"
      ],
      "expansion": "¬d = 0 ∧ (∃ x. ∃ y. ∃ m. n = d · x ∧ (ArithAt(F,d,y) ∧ (ArithAt(G,x,m) ∧ SignedMul(y,m,z)))) ∨ (d = 0 ∨ ¬Dvd(d,n)) ∧ z = 0",
      "expansion_sha256": "49d9a935ac5daa8c3547a524dd283ceeb3aaec5c82dc46f26f64b0c78366e4a7",
      "meaning": "At a positive divisor d, witness n=d*q, read the actual signed values F(d) and G(q), and multiply them. Zero and nondivisors contribute canonical zero without reading either input at zero. Source-table validity is separate.",
      "milestone_users": [],
      "name": "DirichletEntry",
      "parameters": [
        "F",
        "G",
        "n",
        "d",
        "z"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "DirichletEntry",
        "blueprint_parameters": [
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        ],
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        ],
        "reviewed_expansion_sha256": "bac94ba84c7bcfd9ed0346d373efda57556124addff586c0bafd831d2e830bd5",
        "reviewed_id": "ND0301",
        "reviewed_name": "DirichletEntry",
        "reviewed_parameters": [
          "F",
          "G",
          "n",
          "d",
          "z"
        ],
        "route": "dirichlet-convolution"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "ArithAt",
        "BetaAt",
        "Dvd",
        "MatrixMinorFourCode",
        "SignedBalance",
        "SignedDecode",
        "SignedMul"
      ],
      "transitive_dependents": [
        "DirichletCoprimeProductData",
        "DirichletDivisorGridWitness",
        "DirichletInverse",
        "DirichletPrefix",
        "DirichletSum",
        "DirichletTable"
      ]
    },
    {
      "arity": 7,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt",
        "Dvd",
        "SignedMul"
      ],
      "dependents": [
        "DirichletFactorRow",
        "DirichletFlatEntry",
        "DirichletGrid"
      ],
      "expansion": "¬a = 0 ∧ (¬e = 0 ∧ (∃ x. ∃ y. ∃ m. ∃ k. n = a · e · x ∧ (ArithAt(F,a,y) ∧ (ArithAt(H,e,m) ∧ (ArithAt(G,x,k) ∧ (∃ i. SignedMul(m,k,i) ∧ SignedMul(y,i,z))))))) ∨ (a = 0 ∨ (e = 0 ∨ ¬Dvd(a · e,n))) ∧ z = 0",
      "expansion_sha256": "b722404f45619abe88a7673293b6368f94377e372c86e9f04c2e36eae9d99b77",
      "meaning": "A retained cell has a!=0, e!=0, an actual middle factor n=(a*e)*c, and the two signed products F(a)*(H(e)*G(c)). Cells with a=0, e=0 or a*e not dividing n are zero. Positivity of n and source-table validity are separate guards.",
      "milestone_users": [],
      "name": "DirichletGridEntry",
      "parameters": [
        "F",
        "G",
        "H",
        "n",
        "a",
        "e",
        "z"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "DirichletGridEntry",
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          "z"
        ],
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        "reviewed_argument_blueprint_positions": [
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          3,
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        ],
        "reviewed_expansion_sha256": "23df3af9a76be08e77f8e46298fe61b7cf501b97ee0b34c10d27f7fa5d3a8cec",
        "reviewed_id": "ND0305",
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        "reviewed_parameters": [
          "F",
          "G",
          "H",
          "n",
          "a",
          "e",
          "z"
        ],
        "route": "dirichlet-fubini"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "ArithAt",
        "BetaAt",
        "Dvd",
        "MatrixMinorFourCode",
        "SignedBalance",
        "SignedDecode",
        "SignedMul"
      ],
      "transitive_dependents": [
        "DirichletFactorRow",
        "DirichletFlatEntry",
        "DirichletFlatPrefix",
        "DirichletGrid"
      ]
    },
    {
      "arity": 1,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt"
      ],
      "dependents": [],
      "expansion": "ArithAt(F,1,2) ∨ ArithAt(F,1,1)",
      "expansion_sha256": "910df7269edae6fdc23bd2a97554bab7540757a2096fdd13c5ee29b2a104f088",
      "meaning": "An actual lookup F(1) has canonical signed code 2 or 1. This direct disjunction contains ArithAt, not a SignedUnit or inverse subformula. Table validity, the finite window bound, and the inverse criterion are separate hypotheses or theorems.",
      "milestone_users": [],
      "name": "DirichletUnitAtOne",
      "parameters": [
        "F"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
        "blueprint_expansion_is_kernel_checked": false,
        "blueprint_name": "DirichletUnitAtOne",
        "blueprint_parameters": [
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        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "fe5dfe335391ee72e998eff1d7ee83f6a2f5c912e47a486bb663e8c0af99ac49",
        "reviewed_id": "ND0314",
        "reviewed_name": "DirichletUnitAtOne",
        "reviewed_parameters": [
          "F"
        ],
        "route": "dirichlet-inverses"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "ArithAt",
        "BetaAt",
        "MatrixMinorFourCode",
        "SignedBalance",
        "SignedDecode"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ArithAt",
        "Dvd"
      ],
      "dependents": [
        "DivisorMask"
      ],
      "expansion": "¬d = 0 ∧ (∃ x. n = d · x ∧ ArithAt(F,d,z)) ∨ (d = 0 ∨ ¬Dvd(d,n)) ∧ z = 0",
      "expansion_sha256": "b2a17627d0a9b989dd903800cee515207f37493fab4fd7386faec63aca0cf10a",
      "meaning": "A positive d with an actual quotient n=d*q keeps the genuine input value F(d); zero and nondivisors give canonical zero. The zero branch never reads or restricts F(0).",
      "milestone_users": [],
      "name": "DivisorMaskEntry",
      "parameters": [
        "F",
        "n",
        "d",
        "z"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_id": "ND0273",
        "reviewed_name": "DivisorMaskEntry",
        "reviewed_parameters": [
          "F",
          "n",
          "d",
          "z"
        ],
        "route": "divisor-sums"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "ArithAt",
        "BetaAt",
        "Dvd",
        "MatrixMinorFourCode",
        "SignedBalance",
        "SignedDecode"
      ],
      "transitive_dependents": [
        "DivisorMask",
        "DivisorSum",
        "DivisorTransform"
      ]
    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "DivisorPrimeToggle",
        "Lt"
      ],
      "dependents": [],
      "expansion": "∀ dvi_index_lowercontinuation. Lt(dvi_index_lowercontinuation,l) → ∃ x. BetaAt(b,c,dvi_index_lowercontinuation,x) ∧ DivisorPrimeToggle(n,p,dvi_index_lowercontinuation,x)",
      "expansion_sha256": "226b46f085b303c9498576931ead2271b6ddb109525b8bd11489f25fcb630191",
      "meaning": "A real finite beta map witnesses each divisor-prime-toggle output on i<l. No finite-choice, permutation or sum identity is assumed.",
      "milestone_users": [],
      "name": "DivisorPrimeTogglePrefix",
      "parameters": [
        "n",
        "p",
        "b",
        "c",
        "l"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "DivisorPrimeTogglePrefix",
        "blueprint_parameters": [
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        ],
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        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "5a5da490305be5e09e0368ad604edab9af8235871522ae0f88ff00930df4f6fe",
        "reviewed_id": "ND0285",
        "reviewed_name": "DivisorPrimeTogglePrefix",
        "reviewed_parameters": [
          "n",
          "p",
          "b",
          "c",
          "l"
        ],
        "route": "mobius-divisor-cancellation"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "BetaAt",
        "DivisorPrimeToggle",
        "Dvd",
        "Lt",
        "PrimeFactorToggle"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "ZPairRep"
      ],
      "dependents": [
        "EDivRem"
      ],
      "expansion": "∃ ee_first_rp_lowerlayer. ∃ ee_first_rn_lowerlayer. ∃ ee_first_ip_lowerlayer. ∃ ee_first_in_lowerlayer. ∃ ee_second_rp_lowerlayer. ∃ ee_second_rn_lowerlayer. ∃ ee_second_ip_lowerlayer. ∃ ee_second_in_lowerlayer. ZPairRep(a,ee_first_rp_lowerlayer,ee_first_rn_lowerlayer,ee_first_ip_lowerlayer,ee_first_in_lowerlayer) ∧ (ZPairRep(b,ee_second_rp_lowerlayer,ee_second_rn_lowerlayer,ee_second_ip_lowerlayer,ee_second_in_lowerlayer) ∧ ZPairRep(c,ee_first_rp_lowerlayer · ee_second_rp_lowerlayer + ee_first_rn_lowerlayer · ee_second_rn_lowerlayer + (ee_first_ip_lowerlayer · ee_second_in_lowerlayer + ee_first_in_lowerlayer · ee_second_ip_lowerlayer),ee_first_rp_lowerlayer · ee_second_rn_lowerlayer + ee_first_rn_lowerlayer · ee_second_rp_lowerlayer + (ee_first_ip_lowerlayer · ee_second_ip_lowerlayer + ee_first_in_lowerlayer · ee_second_in_lowerlayer),ee_first_rp_lowerlayer · ee_second_ip_lowerlayer + ee_first_rn_lowerlayer · ee_second_in_lowerlayer + (ee_first_ip_lowerlayer · ee_second_rp_lowerlayer + ee_first_in_lowerlayer · ee_second_rn_lowerlayer) + (ee_first_ip_lowerlayer · ee_second_in_lowerlayer + ee_first_in_lowerlayer · ee_second_ip_lowerlayer),ee_first_rp_lowerlayer · ee_second_in_lowerlayer + ee_first_rn_lowerlayer · ee_second_ip_lowerlayer + (ee_first_ip_lowerlayer · ee_second_rn_lowerlayer + ee_first_in_lowerlayer · ee_second_rp_lowerlayer) + (ee_first_ip_lowerlayer · ee_second_ip_lowerlayer + ee_first_in_lowerlayer · ee_second_in_lowerlayer)))",
      "expansion_sha256": "29feac8c066971b2825eaf34d45fde0ddefae8e05201dd6d1f39bacd52525522",
      "meaning": "Actual multiplication in the Eisenstein ring, using the shared signed-pair carrier and the law ω²+ω+1=0.",
      "milestone_users": [],
      "name": "EMul",
      "parameters": [
        "a",
        "b",
        "c"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "EMul",
        "blueprint_parameters": [
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        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "79481871eafd751574ee648c69015cd15cbb8917513e4d04bda63e8d1585cc00",
        "reviewed_id": "ND0172",
        "reviewed_name": "EMul",
        "reviewed_parameters": [
          "a",
          "b",
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        ],
        "route": "eisenstein-integers"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "SignedBalance",
        "SignedDecode",
        "ZPairRep"
      ],
      "transitive_dependents": [
        "EDivRem",
        "EEuclideanDivision"
      ]
    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "EisensteinCoordinateNorm",
        "ZPairRep"
      ],
      "dependents": [
        "EEuclideanDivision"
      ],
      "expansion": "∃ ee_norm_rp_lowerlayer. ∃ ee_norm_rn_lowerlayer. ∃ ee_norm_ip_lowerlayer. ∃ ee_norm_in_lowerlayer. ZPairRep(z,ee_norm_rp_lowerlayer,ee_norm_rn_lowerlayer,ee_norm_ip_lowerlayer,ee_norm_in_lowerlayer) ∧ EisensteinCoordinateNorm(ee_norm_rp_lowerlayer,ee_norm_rn_lowerlayer,ee_norm_ip_lowerlayer,ee_norm_in_lowerlayer,n)",
      "expansion_sha256": "91d3400bc0e82e59656d841fe673b94e331bee67826d63e4239d25353f0644db",
      "meaning": "The actual norm a²−ab+b² of the shared canonical pair code representing the Eisenstein integer a+bω.",
      "milestone_users": [
        "G086"
      ],
      "name": "ENorm",
      "parameters": [
        "z",
        "n"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "ENorm",
        "blueprint_parameters": [
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        ],
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "5f956fea815b9f8e65f510fd1e395a0cfff3cf4c30ea49b487589dfa796f7220",
        "reviewed_id": "ND0171",
        "reviewed_name": "ENorm",
        "reviewed_parameters": [
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        ],
        "route": "eisenstein-integers"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "EisensteinCoordinateNorm",
        "SignedBalance",
        "SignedDecode",
        "ZPairRep"
      ],
      "transitive_dependents": [
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      ]
    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Coprime",
        "Lt",
        "OppositeParity"
      ],
      "dependents": [],
      "expansion": "n≠0 ∧ Lt(n,m) ∧ Coprime(m,n) ∧ OppositeParity(m,n) ∧ c=m*m+n*n ∧ m*m=n*n+a ∧ b=2*(m*n)",
      "expansion_sha256": "fb3eec91379a0fd92121adf406336b6d076c1a714893379ea62d1fd421d8f90a",
      "meaning": "Positive ordered coprime opposite-parity parameters with the odd leg first and all exact coordinate identities.",
      "milestone_users": [
        "G077"
      ],
      "name": "EuclidParameters",
      "parameters": [
        "a",
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        "c",
        "m",
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      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "EuclidParameters",
        "blueprint_parameters": [
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        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "62d005f8054cad7e799c8762a84ff0934f876d6174e1f8c8fc5bb4c54a139c2d",
        "reviewed_id": "ND0070",
        "reviewed_name": "EuclidParameters",
        "reviewed_parameters": [
          "a",
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          "c",
          "m",
          "n"
        ],
        "route": "pythagorean-fermat-four"
      },
      "topological_layer": 3,
      "transitive_dependencies": [
        "Coprime",
        "Dvd",
        "Even",
        "Gcd",
        "Lt",
        "Odd",
        "OppositeParity"
      ],
      "transitive_dependents": []
    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Coprime",
        "Lt",
        "OppositeParity"
      ],
      "dependents": [],
      "expansion": "∃m n. n≠0 ∧ Lt(n,m) ∧ Coprime(m,n) ∧ OppositeParity(m,n) ∧ c=m*m+n*n ∧ ((m*m=n*n+a ∧ b=2*(m*n)) ∨ (m*m=n*n+b ∧ a=2*(m*n)))",
      "expansion_sha256": "6e8bb8380ccb98d3fc82e7f3b589d513c9c0e1b17aebf71909cf6dbdb9b65baa",
      "meaning": "Existence of positive ordered Euclid parameters in either ordered leg orientation.",
      "milestone_users": [
        "G077"
      ],
      "name": "EuclidParametrization",
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        "a",
        "b",
        "c"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "reviewed_id": "ND0074",
        "reviewed_name": "EuclidParametrization",
        "reviewed_parameters": [
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          "c"
        ],
        "route": "pythagorean-fermat-four"
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      "topological_layer": 3,
      "transitive_dependencies": [
        "Coprime",
        "Dvd",
        "Even",
        "Gcd",
        "Lt",
        "Odd",
        "OppositeParity"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 5,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BitLen",
        "EuclideanAnchoredExecution",
        "Le"
      ],
      "dependents": [],
      "expansion": "BitLen(b,ell) ∧ EuclideanAnchoredExecution(a,b,g,k) ∧ Le(k,2*ell+1)",
      "expansion_sha256": "fc9b19fb88b12a33dd8921548a6951ac6bba8cd769dd9e5432899637e874f2df",
      "meaning": "A terminal-state-identified Euclidean gcd execution bounded by twice the exact binary length plus one.",
      "milestone_users": [
        "G101"
      ],
      "name": "EuclideanLogarithmicExecution",
      "parameters": [
        "a",
        "b",
        "ell",
        "g",
        "k"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "EuclideanLogarithmicExecution",
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        ],
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        "reviewed_argument_blueprint_positions": [
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        ],
        "reviewed_expansion_sha256": "8221ba7d4da566d5b0cc31b1771bebeb99136c2c61eebf58c472d9357c30bb27",
        "reviewed_id": "ND0039",
        "reviewed_name": "EuclideanLogarithmicExecution",
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        "route": "euclidean-logarithmic-bound"
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      "transitive_dependencies": [
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        "ContinuedFractionTrace",
        "Dvd",
        "EuclideanAnchoredExecution",
        "EuclideanStateAt",
        "Gcd",
        "Le",
        "ListCell",
        "Lt",
        "Pow",
        "PowTwo"
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      "transitive_dependents": []
    },
    {
      "arity": 7,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "EulerPrimePowerFactor",
        "Lt"
      ],
      "dependents": [
        "EulerProduct"
      ],
      "expansion": "∀ eutprod_index_prioritylayer. Lt(eutprod_index_prioritylayer,l) → ∃ x. ∃ y. ∃ z. BetaAt(pb,pc,eutprod_index_prioritylayer,x) ∧ (BetaAt(eb,ec,eutprod_index_prioritylayer,y) ∧ (BetaAt(fb,fc,eutprod_index_prioritylayer,z) ∧ EulerPrimePowerFactor(x,y,z)))",
      "expansion_sha256": "488850bc8fc30a2962de3ec740ce44313e55252e037d67f9c82d2b05ba49943b",
      "meaning": "At every bounded index, the same prime/exponent entries determine the actual Euler factor in the third beta prefix.",
      "milestone_users": [],
      "name": "EulerFactorPrefix",
      "parameters": [
        "pb",
        "pc",
        "eb",
        "ec",
        "fb",
        "fc",
        "l"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "EulerFactorPrefix",
        "blueprint_parameters": [
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          "pc",
          "eb",
          "ec",
          "fb",
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          "l"
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        "kind": "exact-name",
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      "topological_layer": 3,
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      "expansion": "∀ pfs_index_polynomial_division_definition. Lt(pfs_index_polynomial_division_definition,L) → ∃ x. ∃ y. BetaAt(ab,ac,pfs_index_polynomial_division_definition,x) ∧ (BetaAt(rb,rc,pfs_index_polynomial_division_definition,y) ∧ FpAdd(p,x,y,0))",
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      "name": "FpCoefficientNegation",
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      "expansion": "∀ pfs_index_polynomial_division_definition. Lt(pfs_index_polynomial_division_definition,L) → ∃ x. ∃ y. ∃ z. BetaAt(ab,ac,pfs_index_polynomial_division_definition,x) ∧ (BetaAt(bb,bc,pfs_index_polynomial_division_definition,y) ∧ (BetaAt(rb,rc,pfs_index_polynomial_division_definition,z) ∧ FpAdd(p,y,z,x)))",
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      "meaning": "An actual bounded additive inverse: FpAdd(p,a,b,0). Its existence and uniqueness are theorems.",
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      "expansion": "∀ pft_index_bottomlayer. Lt(pft_index_bottomlayer,l) → ∃ x. BetaAt(b,c,pft_index_bottomlayer,x) ∧ FpAdd(p,pft_index_bottomlayer,x,0)",
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      "meaning": "The actual beta prefix records an additive inverse for each index below l.",
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      "expansion": "∀ pfp_index_lowertier. Lt(pfp_index_lowertier,l) → ∃ x. ∃ y. ∃ z. BetaAt(ab,ac,pfp_index_lowertier,x) ∧ (BetaAt(bb,bc,pfp_index_lowertier,y) ∧ (BetaAt(cb,cc,pfp_index_lowertier,z) ∧ FpAdd(p,x,y,z)))",
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        "route": "prime-fields"
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        "FpUnitTrace"
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    },
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      "expansion": "∃ ge_first_rp_lowerlayer. ∃ ge_first_rn_lowerlayer. ∃ ge_first_ip_lowerlayer. ∃ ge_first_in_lowerlayer. ∃ ge_second_rp_lowerlayer. ∃ ge_second_rn_lowerlayer. ∃ ge_second_ip_lowerlayer. ∃ ge_second_in_lowerlayer. ZPairRep(a,ge_first_rp_lowerlayer,ge_first_rn_lowerlayer,ge_first_ip_lowerlayer,ge_first_in_lowerlayer) ∧ (ZPairRep(b,ge_second_rp_lowerlayer,ge_second_rn_lowerlayer,ge_second_ip_lowerlayer,ge_second_in_lowerlayer) ∧ ZPairRep(c,ge_first_rp_lowerlayer · ge_second_rp_lowerlayer + ge_first_rn_lowerlayer · ge_second_rn_lowerlayer + (ge_first_ip_lowerlayer · ge_second_in_lowerlayer + ge_first_in_lowerlayer · ge_second_ip_lowerlayer),ge_first_rp_lowerlayer · ge_second_rn_lowerlayer + ge_first_rn_lowerlayer · ge_second_rp_lowerlayer + (ge_first_ip_lowerlayer · ge_second_ip_lowerlayer + ge_first_in_lowerlayer · ge_second_in_lowerlayer),ge_first_rp_lowerlayer · ge_second_ip_lowerlayer + ge_first_rn_lowerlayer · ge_second_in_lowerlayer + (ge_first_ip_lowerlayer · ge_second_rp_lowerlayer + ge_first_in_lowerlayer · ge_second_rn_lowerlayer),ge_first_rp_lowerlayer · ge_second_in_lowerlayer + ge_first_rn_lowerlayer · ge_second_ip_lowerlayer + (ge_first_ip_lowerlayer · ge_second_rn_lowerlayer + ge_first_in_lowerlayer · ge_second_rp_lowerlayer)))",
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      "meaning": "Actual Gaussian multiplication: (a+bi)(c+di)=(ac−bd)+(ad+bc)i, with canonical pair-code outputs.",
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      "expansion": "∃ ge_norm_rp_lowerlayer. ∃ ge_norm_rn_lowerlayer. ∃ ge_norm_ip_lowerlayer. ∃ ge_norm_in_lowerlayer. ZPairRep(z,ge_norm_rp_lowerlayer,ge_norm_rn_lowerlayer,ge_norm_ip_lowerlayer,ge_norm_in_lowerlayer) ∧ GaussianSignedNorm(ge_norm_rp_lowerlayer,ge_norm_rn_lowerlayer,ge_norm_ip_lowerlayer,ge_norm_in_lowerlayer,n)",
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      "expansion": "∃n. HornerDerivative(b,c,t,l,n,z)",
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      "meaning": "The exact formal derivative of a beta-coded finite natural polynomial at the supplied evaluation point.",
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      "expansion": "BetaAt(b,c,0,2) ∧ (∀ x. Lt(x,k) → ∃ y. ∃ z. BetaAt(b,c,x,y) ∧ (BetaAt(b,c,S x,z) ∧ NextPrime(y,z)))",
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      "dependents": [],
      "expansion": "∀ dp_i. Lt(dp_i,k) → ∃ x. BetaAt(b,c,dp_i,x) ∧ InverseIndex(m,l,dp_i,x)",
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        "route": "quadratic-reciprocity"
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      "expansion": "n is positive and odd, Coprime(a,n), and s is the factorwise quadratic-bit sum modulo two",
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      "expansion": "ArithTable(N,E) ∧ (∀ x. ∀ y. ¬x = 0 → Le(x,N) → ArithAt(E,x,y) → (x = 1 → y = 2) ∧ (¬x = 1 → y = 0))",
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      "transitive_dependents": [
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      "authority": "blueprint-vocabulary-only",
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        "Le",
        "Mobius"
      ],
      "dependents": [],
      "expansion": "∀ mdc_positive_index_lowercontinuation. ∀ mdc_positive_value_lowercontinuation. ¬mdc_positive_index_lowercontinuation = 0 → Le(mdc_positive_index_lowercontinuation,N) → ArithAt(F,mdc_positive_index_lowercontinuation,mdc_positive_value_lowercontinuation) → Mobius(mdc_positive_index_lowercontinuation,mdc_positive_value_lowercontinuation)",
      "expansion_sha256": "cef73b2f6034afb5f9181acfb8f740c00aaf1fe3201a3929fa9509e8a0606916",
      "meaning": "Every actual positive entry through N agrees with the independently defined Möbius function. Table validity is separate and F(0) is unrestricted; the historical MobiusTable zero convention remains unchanged.",
      "milestone_users": [],
      "name": "MobiusPositiveValues",
      "parameters": [
        "N",
        "F"
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "MobiusPositiveValues",
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        "reviewed_id": "ND0299",
        "reviewed_name": "MobiusPositiveValues",
        "reviewed_parameters": [
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        "route": "mobius-divisor-cancellation"
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      "topological_layer": 3,
      "transitive_dependencies": [
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        "BetaAt",
        "Le",
        "MatrixMinorFourCode",
        "Mobius",
        "SignedBalance",
        "SignedDecode"
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      "transitive_dependents": []
    },
    {
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      "dependencies": [
        "ArithAt",
        "ArithTable",
        "Le",
        "Mobius"
      ],
      "dependents": [],
      "expansion": "ArithTable(N,M) ∧ (ArithAt(M,0,0) ∧ (∀ x. ∀ y. ¬x = 0 → Le(x,N) → ArithAt(M,x,y) → Mobius(x,y)))",
      "expansion_sha256": "e8dae3cbed59a06db202903e085c7d61d0ff2eeb6210805d059680074754f955",
      "meaning": "A genuine table through N records zero at index zero and the independently defined Möbius value at every positive index through N. The zero-table convention does not extend Mobius to input zero.",
      "milestone_users": [
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      "name": "MobiusTable",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "reviewed_name": "MobiusTable",
        "reviewed_parameters": [
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        "route": "divisor-sums"
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      "transitive_dependencies": [
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        "Le",
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    {
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      "dependencies": [
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        "MultinomialBinomialPrefix",
        "Product"
      ],
      "dependents": [],
      "expansion": "∃ mkm_sum_code_secondwave. ∃ mkm_sum_scale_secondwave. ∃ mkm_factor_code_secondwave. ∃ mkm_factor_scale_secondwave. BetaSumTrace(b,c,l,n,mkm_sum_code_secondwave,mkm_sum_scale_secondwave) ∧ (MultinomialBinomialPrefix(b,c,mkm_sum_code_secondwave,mkm_sum_scale_secondwave,mkm_factor_code_secondwave,mkm_factor_scale_secondwave,l) ∧ Product(mkm_factor_code_secondwave,mkm_factor_scale_secondwave,l,z))",
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      "meaning": "An actual list of parts with total n, a running sum, and the finite product of its iterated binomial factors; the empty product is one.",
      "milestone_users": [
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      "name": "Multinomial",
      "parameters": [
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        "l",
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        "z"
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        "blueprint_name": "Multinomial",
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        "route": "multinomial-kummer"
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      "dependencies": [
        "ArithAt",
        "ArithTable",
        "Coprime",
        "Le",
        "SignedMul"
      ],
      "dependents": [
        "DirichletCoprimeProductData"
      ],
      "expansion": "¬N = 0 ∧ (ArithTable(N,F) ∧ (ArithAt(F,1,2) ∧ (∀ x. ∀ y. ∀ z. ∀ n. ∀ m. ¬x = 0 → ¬y = 0 → Le(x · y,N) → Coprime(x,y) → ArithAt(F,x,z) → ArithAt(F,y,n) → ArithAt(F,x · y,m) → SignedMul(z,n,m))))",
      "expansion_sha256": "29a65fc55e431214d31f0562f60767a43ac7cbb0a086e8f92ab8370ada9cf7de",
      "meaning": "An actual nonempty signed prefix, N>0, has F(1)=+1 (canonical code 2) and the signed product law for positive coprime a,b with a*b<=N. F(0) and values outside that window remain unrestricted. Signed-unit codes plus or minus one are not this normalization; the one-argument planning notation Multiplicative(f) is not an alias.",
      "milestone_users": [
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      "name": "MultiplicativePrefix",
      "parameters": [
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        "reviewed_name": "MultiplicativePrefix",
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        "route": "multiplicative-convolution"
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      "transitive_dependencies": [
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        "Dvd",
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        "SignedBalance",
        "SignedDecode",
        "SignedMul"
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      "transitive_dependents": [
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      "expansion": "Squarefree(r) ∧ n = r · (s · s)",
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      "meaning": "An actual squarefree natural r and the balance n=r·s². This is not the blueprint's unrelated polynomial SquarefreeDecomposition predicate.",
      "milestone_users": [],
      "name": "NaturalSquarefreeDecomposition",
      "parameters": [
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        "blueprint_name": "NaturalSquarefreeDecomposition",
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        "reviewed_name": "NaturalSquarefreeDecomposition",
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        "route": "squarefree-kernels"
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      "transitive_dependencies": [
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      "dependencies": [
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      "expansion": "∀ pfc_index_lowercontinuation. Lt(pfc_index_lowercontinuation,l) → ∃ x. BetaAt(db,dc,pfc_index_lowercontinuation,x) ∧ PolynomialDiagonalTerm(ab,ac,L,bb,bc,M,i,pfc_index_lowercontinuation,x)",
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      "meaning": "A real beta table contains the actual antidiagonal products for j<l. The full window l=S i is constructed, so every complementary index is natural.",
      "milestone_users": [],
      "name": "PolynomialDiagonalPrefix",
      "parameters": [
        "ab",
        "ac",
        "L",
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        "bc",
        "M",
        "i",
        "db",
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        "reviewed_id": "ND0293",
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          "i",
          "db",
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        "route": "polynomial-products"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      "dependents": [
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      "expansion": "Val(p,n,e)",
      "expansion_sha256": "38e0ff09a37a7913ffb000024e833cea9c2e616f6ccc480b5af88d89af3d7175",
      "meaning": "Conservative named alias for the exact positive-input prime-power valuation.",
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      "name": "PowerValuation",
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        "route": "bertrand-postulate"
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      "transitive_dependencies": [
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      "transitive_dependents": [
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      "dependencies": [
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      "dependents": [
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      "expansion": "∀ pvs_index_prioritylayer. Lt(pvs_index_prioritylayer,l) → ∃ x. ∃ y. ∃ z. BetaAt(pb,pc,pvs_index_prioritylayer,x) ∧ (BetaAt(eb,ec,pvs_index_prioritylayer,y) ∧ (BetaAt(vb,vc,pvs_index_prioritylayer,z) ∧ (Prime(x) ∧ (¬y = 0 ∧ (BoundedPowerValuation(x,n,n,y) ∧ Pow(x,y,z))))))",
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      "meaning": "Each bounded index simultaneously decodes an actual prime, its positive valuation in n, and the value of that prime power.",
      "milestone_users": [],
      "name": "PrimeExponentEntries",
      "parameters": [
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        "pb",
        "pc",
        "eb",
        "ec",
        "vb",
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      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "PrimeExponentEntries",
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        "reviewed_name": "PrimeExponentEntries",
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      "dependencies": [
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      "expansion": "¬n = 0 ∧ (Product(b,c,l,n) ∧ AllPrime(b,c,l))",
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      "meaning": "A positive number n, an actual length-l beta product equal to n, and prime entries. No sortedness or supplied canonicalization is required.",
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      "dependencies": [
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      "expansion": "l = m ∧ (PermutationPrefix(u,v,l) ∧ FactorListMatching(b,c,d,e,u,v,l))",
      "expansion_sha256": "f952d6457e758a564e7389fee8ba98b10b5b3bf3906a76bac348bebc7258c7e2",
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      "milestone_users": [
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      "name": "PrimeFactorListPermutation",
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      "expansion": "Prime(p) ∧ ¬n = 0 ∧ BoundedPowerValuation(p,n,n,e)",
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      "meaning": "p is prime, n is nonzero, and e is the bounded p-adic valuation of n.",
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      "expansion": "∀ ppf_prime_prioritylayer. ∀ ppf_exponent_prioritylayer. Prime(ppf_prime_prioritylayer) → BoundedPowerValuation(ppf_prime_prioritylayer,n,n,ppf_exponent_prioritylayer) → Dvd(k,ppf_exponent_prioritylayer)",
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      "expansion": "Pythagorean(x,y,z) ∧ Coprime(x,y)",
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      "expansion": "Lt(i,l) ∧ ScaledInverse(m,t,S i,y)",
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      "meaning": "i indexes a bounded unit mapped to y by scaled inversion.",
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      "expansion": "∃ub uc vb vc. SignedAlternatingProductPrefix(ab,ac,db,dc,eb,ec,fb,fc,ub,uc,vb,vc,l) ∧ BetaSum(ub,uc,l,p) ∧ BetaSum(vb,vc,l,n)",
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      "expansion": "ArithTable(0,F) ∧ (ArithTable(0,G) ∧ (ArithTable(m · n,T) ∧ (∀ x. ∀ y. ∀ z. ∀ k. ∀ i. Lt(x,m) → Lt(y,n) → ArithAt(F,x,z) → ArithAt(G,y,k) → ArithAt(T,n · x + y,i) → SignedMul(z,k,i))))",
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      "expansion": "HornerDerivative(pb,pc,a,l,vp,dp) ∧ HornerDerivative(nb,nc,a,l,vn,dn)",
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      "meaning": "Two actual natural Horner value/derivative pairs represent the integer value vp−vn and derivative dp−dn.",
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      "dependents": [
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      "expansion": "∃ ssr_entry_value_g009_definition. ∃ ssr_entry_image_g009_definition. ArithAt(A,i,ssr_entry_value_g009_definition) ∧ (BetaAt(r,s,i,ssr_entry_image_g009_definition) ∧ (j = ssr_entry_image_g009_definition ∧ z = ssr_entry_value_g009_definition ∨ ¬j = ssr_entry_image_g009_definition ∧ z = 0))",
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      "meaning": "Read the actual signed source value at i and its actual native beta image. The cell equals that value when j is the image and equals zero otherwise. No reindexing, table-construction or sum conclusion is assumed.",
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      "expansion": "ArithTable(0,A) ∧ (ArithTable(0,B) ∧ ((∀ x. ∀ y. Lt(x,L) → ArithAt(A,x,y) → ¬y = 0 → ∃ z. BetaAt(r,s,x,z) ∧ (Lt(z,M) ∧ ArithAt(B,z,y))) ∧ ((∀ x. ∀ y. ∀ z. ∀ n. ∀ m. Lt(x,L) → Lt(y,L) → ArithAt(A,x,n) → ¬n = 0 → ArithAt(A,y,m) → ¬m = 0 → BetaAt(r,s,x,z) → BetaAt(r,s,y,z) → x = y) ∧ (∀ x. ∀ y. Lt(x,M) → ArithAt(B,x,y) → ¬y = 0 → ∃ z. Lt(z,L) ∧ (BetaAt(r,s,z,x) ∧ ArithAt(A,z,y))))))",
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      "expansion": "∃ hpl_value_secondwave. ∃ hpl_derivative_secondwave. HornerDerivative(b,c,a,l,hpl_value_secondwave,hpl_derivative_secondwave) ∧ (ModEq(m,hpl_value_secondwave,0) ∧ Coprime(hpl_derivative_secondwave,p))",
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      "expansion": "∀ eut_index_prioritylayer. Lt(eut_index_prioritylayer,l) → ∃ x. BetaAt(b,c,eut_index_prioritylayer,x) ∧ (Coprime(eut_index_prioritylayer,n) ∧ x = 1 ∨ ¬Coprime(eut_index_prioritylayer,n) ∧ x = 0)",
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      "meaning": "The actual row-major (S n)-by-(S n) factor grid specifies cells a,e<=n at index (S n)*a+e. The underlying table separately certifies its unused endpoint (S n)*(S n). Construction from a flat prefix is a proof dependency, not an extra definition condition.",
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      "expansion": "∀ pft_index_bottomlayer. Lt(pft_index_bottomlayer,l) → ∃ x. BetaAt(b,c,pft_index_bottomlayer,x) ∧ FpAddGridValue(p,pft_index_bottomlayer,x)",
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      "meaning": "Every genuine beta entry below l gives the addition grid value at its actual index.",
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      "meaning": "Build the S i antidiagonal terms, take their actual natural Sum, then take its canonical residue r modulo p. No evaluation-product identity or degree assertion is assumed.",
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        "bb",
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      "expansion": "BetaAt(b,c,0,0) ∧ (BetaAt(b,c,n,r) ∧ FpUnitSteps(p,b,c,n))",
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      "expansion": "∀ mkm_index_secondwave. Lt(mkm_index_secondwave,l) → ∃ x. ∃ y. ∃ z. BetaAt(b,c,mkm_index_secondwave,x) ∧ (BetaAt(sb,sc,mkm_index_secondwave,y) ∧ (BetaAt(vb,vc,mkm_index_secondwave,z) ∧ BinaryColumnCarryCount(p,y,x,z)))",
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      "expansion": "¬n = 0 ∧ (InjectivePrefix(pb,pc,l) ∧ (PrimeExponentEntries(n,pb,pc,eb,ec,vb,vc,l) ∧ (PrimeDivisorSupport(n,pb,pc,l) ∧ Product(vb,vc,l,n))))",
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      "meaning": "A positive primitive ordered Pythagorean triple in either leg orientation.",
      "milestone_users": [
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      "expansion": "∀ dp_i. Lt(dp_i,k) → ∃ x. BetaAt(b,c,dp_i,x) ∧ ScaledInverseIndex(m,t,l,dp_i,x)",
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      "meaning": "A beta prefix decodes a scaled inverse map.",
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        "route": "quadratic-reciprocity"
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      "arity": 11,
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      "dependencies": [
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      "dependents": [],
      "expansion": "∃ab ac db dc. MatrixAffineSlice(pb,pc,0,1,ab,ac,S(q)) ∧ MatrixAffineSlice(nb,nc,0,1,db,dc,S(q)) ∧ SignedAlternatingCofactorFold(ab,ac,db,dc,eb,ec,fb,fc,S(q),p,n)",
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      "meaning": "An exact arbitrary-dimensional signed alternating cofactor fold using the actual decoded positive and negative first row of the input matrix.",
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      "parameters": [
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        "route": "matrix-cofactor-expansion"
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      "expansion": "∃ ssr_flat_row_g009_definition. ∃ ssr_flat_column_g009_definition. k = S M · ssr_flat_row_g009_definition + ssr_flat_column_g009_definition ∧ (Lt(ssr_flat_column_g009_definition,S M) ∧ SignedIncidenceEntry(A,r,s,ssr_flat_row_g009_definition,ssr_flat_column_g009_definition,z))",
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      "meaning": "Witness actual quotient/remainder coordinates k=(S M)*i+j with j<S M, then read the independently defined incidence cell. Physical stride S M remains positive when M=0; this graph has no upper row bound.",
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      "name": "SignedIncidenceFlatEntry",
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      "expansion": "MatrixMinorPrefix(pb,pc,w,r,d,up,us,q,q*q) ∧ MatrixMinorPrefix(nb,nc,w,r,d,un,ut,q,q*q)",
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      "meaning": "An exact arbitrary-dimensional signed matrix minor with independently coded positive and negative components.",
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      "meaning": "A full arbitrary-dimensional signed matrix product with independently beta-coded positive and negative output matrices.",
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      "name": "SignedMatrixProduct",
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      "dependencies": [
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      "expansion": "∃ hsc_vp_secondwave. ∃ hsc_dp_secondwave. ∃ hsc_vn_secondwave. ∃ hsc_dn_secondwave. SignedHornerValueDerivative(pb,pc,nb,nc,a,l,hsc_vp_secondwave,hsc_dp_secondwave,hsc_vn_secondwave,hsc_dn_secondwave) ∧ (ModEq(m,hsc_vp_secondwave,hsc_vn_secondwave) ∧ SignedDerivativeNonzero(p,hsc_dp_secondwave,hsc_dn_secondwave))",
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      "meaning": "An actual integer-polynomial root modulo m whose actual signed derivative is nonzero modulo p; the prime-field inverse is a theorem conclusion.",
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      "name": "SignedNonsingularHornerRoot",
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        "route": "hensel-lifting"
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      "expansion": "∃ sph_vp_secondwave. ∃ sph_dp_secondwave. ∃ sph_vn_secondwave. ∃ sph_dn_secondwave. SignedHornerValueDerivative(pb,pc,nb,nc,a,l,sph_vp_secondwave,sph_dp_secondwave,sph_vn_secondwave,sph_dn_secondwave) ∧ (ModEq(m,sph_vp_secondwave,sph_vn_secondwave) ∧ SignedDerivativeUnit(p,sph_dp_secondwave,sph_dn_secondwave))",
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      "expansion": "∃ srs_slice_lowercontinuation. ArithSlice(F,srs_slice_lowercontinuation,o,s,l) ∧ SignedPrefixSum(srs_slice_lowercontinuation,l,z)",
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        "route": "rectangular-sums"
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      "expansion": "ArithTable(0,A) ∧ (ArithTable(L · S M,T) ∧ (∀ x. ∀ y. ∀ z. Lt(x,L) → Lt(y,M) → ArithAt(T,S M · x + y,z) → SignedIncidenceEntry(A,r,s,x,y,z)))",
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      "dependents": [],
      "expansion": "∃ sws_product_table_lowertier. ArithMul(W,F,sws_product_table_lowertier,l) ∧ SignedPrefixSum(sws_product_table_lowertier,l,z)",
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      "meaning": "An actual signed pointwise product table of weights W and values F, followed by its real signed prefix sum at indices i<l. No linearity, divisor cancellation or inversion is assumed in this graph.",
      "milestone_users": [],
      "name": "SignedWeightedSum",
      "parameters": [
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        "F",
        "l",
        "z"
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      "reviewed_incompatibility": null,
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      "expansion": "∃ eut_code_prioritylayer. ∃ eut_scale_prioritylayer. UnitBitPrefix(n,eut_code_prioritylayer,eut_scale_prioritylayer,l) ∧ BetaSum(eut_code_prioritylayer,eut_scale_prioritylayer,l,t)",
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      "expansion": "∀ eu_factor_index_bottomlayer. Lt(eu_factor_index_bottomlayer,l) → ∃ x. BetaAt(b,c,eu_factor_index_bottomlayer,x) ∧ UnitProductFactor(m,eu_factor_index_bottomlayer,x)",
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      "dependents": [
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      "expansion": "ArithTable(0,F) ∧ (ArithTable(m,R) ∧ (∀ x. Lt(x,m) → ∃ y. ArithAt(R,x,y) ∧ SignedSliceSum(F,o + s · x,t,n,y)))",
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        "route": "binary-digit-extraction"
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      "expansion": "∃ mkm_total_secondwave. ∃ mkm_sb_secondwave. ∃ mkm_sc_secondwave. ∃ mkm_cb_secondwave. ∃ mkm_cc_secondwave. BetaSumTrace(b,c,l,mkm_total_secondwave,mkm_sb_secondwave,mkm_sc_secondwave) ∧ (MultinomialCarryPrefix(p,b,c,mkm_sb_secondwave,mkm_sc_secondwave,mkm_cb_secondwave,mkm_cc_secondwave,l) ∧ BetaSum(mkm_cb_secondwave,mkm_cc_secondwave,l,e))",
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      "expansion": "MultiplicativePrefix(N,F) ∧ (MultiplicativePrefix(N,G) ∧ (¬m = 0 ∧ (¬n = 0 ∧ (Le(m · n,N) ∧ (Coprime(m,n) ∧ (DirichletPrefix(F,G,m,m,A) ∧ (DirichletPrefix(F,G,n,n,B) ∧ (SignedCartesianProduct(A,B,T,S m,S n) ∧ (DirichletPrefix(F,G,m · n,m · n,Q) ∧ DivisorPairIndexMap(S n,S m · S n,r,s))))))))))",
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        "reviewed_id": "ND0174",
        "reviewed_name": "EEuclideanDivision",
        "reviewed_parameters": [
          "a",
          "b",
          "q",
          "r",
          "U",
          "V"
        ],
        "route": "eisenstein-integers"
      },
      "topological_layer": 5,
      "transitive_dependencies": [
        "EDivRem",
        "EMul",
        "ENorm",
        "EisensteinCoordinateNorm",
        "Lt",
        "SignedBalance",
        "SignedDecode",
        "ZPairAdd",
        "ZPairRep"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "EulerFactorPrefix",
        "PrimeValuationSupport",
        "Product"
      ],
      "dependents": [],
      "expansion": "∃ eutprod_prime_code_prioritylayer. ∃ eutprod_prime_scale_prioritylayer. ∃ eutprod_exponent_code_prioritylayer. ∃ eutprod_exponent_scale_prioritylayer. ∃ eutprod_power_code_prioritylayer. ∃ eutprod_power_scale_prioritylayer. ∃ eutprod_length_prioritylayer. ∃ eutprod_factor_code_prioritylayer. ∃ eutprod_factor_scale_prioritylayer. PrimeValuationSupport(n,eutprod_prime_code_prioritylayer,eutprod_prime_scale_prioritylayer,eutprod_exponent_code_prioritylayer,eutprod_exponent_scale_prioritylayer,eutprod_power_code_prioritylayer,eutprod_power_scale_prioritylayer,eutprod_length_prioritylayer) ∧ (EulerFactorPrefix(eutprod_prime_code_prioritylayer,eutprod_prime_scale_prioritylayer,eutprod_exponent_code_prioritylayer,eutprod_exponent_scale_prioritylayer,eutprod_factor_code_prioritylayer,eutprod_factor_scale_prioritylayer,eutprod_length_prioritylayer) ∧ Product(eutprod_factor_code_prioritylayer,eutprod_factor_scale_prioritylayer,eutprod_length_prioritylayer,t))",
      "expansion_sha256": "3276fd9b17eae199e3674ad8d77e9715d5f76d89fe9111e603505dc65a38f5c2",
      "meaning": "A complete distinct prime-valuation support, its independently computed Euler factors, and their actual product t. Equality with Phi is a theorem, not a definition.",
      "milestone_users": [
        "G006"
      ],
      "name": "EulerProduct",
      "parameters": [
        "n",
        "t"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "EulerProduct",
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        ],
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        "reviewed_id": "ND0187",
        "reviewed_name": "EulerProduct",
        "reviewed_parameters": [
          "n",
          "t"
        ],
        "route": "totient-products"
      },
      "topological_layer": 5,
      "transitive_dependencies": [
        "BetaAt",
        "BoundedPowerValuation",
        "Dvd",
        "EulerFactorPrefix",
        "EulerPrimePowerFactor",
        "InjectivePrefix",
        "Le",
        "Lt",
        "Pow",
        "PowerDivides",
        "Prime",
        "PrimeDivisorSupport",
        "PrimeExponentEntries",
        "PrimeValuationSupport",
        "Product"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 10,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "FpConvolutionCoefficient",
        "Lt"
      ],
      "dependents": [
        "FpPolyProduct"
      ],
      "expansion": "∀ pfc_index_lowercontinuation. Lt(pfc_index_lowercontinuation,l) → ∃ x. BetaAt(cb,cc,pfc_index_lowercontinuation,x) ∧ FpConvolutionCoefficient(p,ab,ac,L,bb,bc,M,pfc_index_lowercontinuation,x)",
      "expansion_sha256": "469130a33e234f4a72a9081eea99cbc0e061781497d934d9be4999628240da0c",
      "meaning": "Every output coefficient at i<l is the independently defined actual antidiagonal sum residue. The finite output beta table is constructed rather than postulated.",
      "milestone_users": [],
      "name": "FpConvolutionPrefix",
      "parameters": [
        "p",
        "ab",
        "ac",
        "L",
        "bb",
        "bc",
        "M",
        "cb",
        "cc",
        "l"
      ],
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        "blueprint_name": "FpConvolutionPrefix",
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          "bb",
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        "reviewed_id": "ND0295",
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          "L",
          "bb",
          "bc",
          "M",
          "cb",
          "cc",
          "l"
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        "route": "polynomial-products"
      },
      "topological_layer": 5,
      "transitive_dependencies": [
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        "BetaAt",
        "BetaSum",
        "BetaZeroExtend",
        "CanonicalModularResidue",
        "FpConvolutionCoefficient",
        "Le",
        "Lt",
        "Mod",
        "PolynomialDiagonalPrefix",
        "PolynomialDiagonalTerm"
      ],
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    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "FpHornerSteps",
        "Lt"
      ],
      "dependents": [
        "FpHorner",
        "FpSyntheticDivision"
      ],
      "expansion": "Lt(x,p) ∧ (BetaAt(u,v,0,0) ∧ (BetaAt(u,v,l,r) ∧ FpHornerSteps(p,b,c,x,l,u,v)))",
      "expansion_sha256": "26d0bc31eb11a846762b27e976fe9bb1ab9c7a2d8d6749f225bd442e253aeb74",
      "meaning": "A canonical argument x<p and a real history starting at zero, taking l actual modular Horner steps and ending at r. The argument bound remains present even for the empty zero polynomial.",
      "milestone_users": [],
      "name": "FpHornerTrace",
      "parameters": [
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        "b",
        "c",
        "x",
        "l",
        "r",
        "u",
        "v"
      ],
      "reviewed_incompatibility": null,
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        "blueprint_name": "FpHornerTrace",
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        "reviewed_id": "ND0279",
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        ],
        "route": "prime-field-polynomials"
      },
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      "transitive_dependencies": [
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        "FpAdd",
        "FpHornerStep",
        "FpHornerSteps",
        "FpMul",
        "Lt",
        "Mod"
      ],
      "transitive_dependents": [
        "FpHorner",
        "FpSyntheticDivision"
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    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "FpZeroExtendedInv",
        "Lt"
      ],
      "dependents": [
        "FpOperationTables"
      ],
      "expansion": "∀ pft_index_bottomlayer. Lt(pft_index_bottomlayer,l) → ∃ x. BetaAt(b,c,pft_index_bottomlayer,x) ∧ FpZeroExtendedInv(p,pft_index_bottomlayer,x)",
      "expansion_sha256": "4471a71cc5694e079c702e209e799dd486a1b194aed7ed92857939ba1043bfce",
      "meaning": "The actual beta prefix records the zero-extended inverse function. The nonzero inverse laws are separate theorems.",
      "milestone_users": [],
      "name": "FpInvPrefix",
      "parameters": [
        "p",
        "b",
        "c",
        "l"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "FpInvPrefix",
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        "reviewed_id": "ND0249",
        "reviewed_name": "FpInvPrefix",
        "reviewed_parameters": [
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        "route": "prime-fields"
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      "topological_layer": 5,
      "transitive_dependencies": [
        "BetaAt",
        "CanonicalModularResidue",
        "FpInv",
        "FpMul",
        "FpZeroExtendedInv",
        "Lt",
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      "transitive_dependents": [
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    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "FpUnitTrace"
      ],
      "dependents": [
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      ],
      "expansion": "∃ pff_history_code_bottomlayer. ∃ pff_history_scale_bottomlayer. FpUnitTrace(p,pff_history_code_bottomlayer,pff_history_scale_bottomlayer,n,r)",
      "expansion_sha256": "e501e16eee088e3a312552c1b6d4c9621bb22908280070e87631c1afb82777e6",
      "meaning": "Existence of a genuine n-step addition-of-one history with endpoint r; this is not a restatement of divisibility or characteristic.",
      "milestone_users": [],
      "name": "FpUnitMultiple",
      "parameters": [
        "p",
        "n",
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        "blueprint_name": "FpUnitMultiple",
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        "route": "prime-fields"
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      "transitive_dependencies": [
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        "CanonicalModularResidue",
        "FpAdd",
        "FpUnitSteps",
        "FpUnitTrace",
        "Lt",
        "Mod"
      ],
      "transitive_dependents": [
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        "FpFiniteStructure"
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    },
    {
      "arity": 6,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "GDivRem",
        "GNorm",
        "Lt",
        "ZPairValid"
      ],
      "dependents": [],
      "expansion": "ZPairValid(q) ∧ (ZPairValid(r) ∧ (GDivRem(a,b,q,r) ∧ (GNorm(r,U) ∧ (GNorm(b,V) ∧ Lt(U,V)))))",
      "expansion_sha256": "2205763e2ddfa9e785934eb3cfbc4020aed5ce0712fc7ecf87e66e7e253fcfd5",
      "meaning": "Valid quotient and remainder codes satisfy the genuine Gaussian equation a=bq+r and have actual norms U=N(r), V=N(b) with U<V.",
      "milestone_users": [
        "G081"
      ],
      "name": "GEuclideanDivision",
      "parameters": [
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      ],
      "reviewed_incompatibility": null,
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        "blueprint_name": "GEuclideanDivision",
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        "reviewed_id": "ND0168",
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        ],
        "route": "gaussian-integers"
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      "transitive_dependencies": [
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        "GMul",
        "GNorm",
        "GaussianSignedNorm",
        "Lt",
        "SignedBalance",
        "SignedDecode",
        "SignedDifferenceSquare",
        "ZPairAdd",
        "ZPairDecode",
        "ZPairRep",
        "ZPairValid"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 3,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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      ],
      "dependents": [],
      "expansion": "GDvd(g,a) ∧ (GDvd(g,b) ∧ (∀ x. GDvd(x,a) → GDvd(x,b) → GDvd(x,g)))",
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      "meaning": "g actually divides a and b, and every actual common Gaussian divisor divides g. Literal uniqueness or normalization is not assumed.",
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        "route": "gaussian-factorization"
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      "dependencies": [
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        "Lt"
      ],
      "dependents": [
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      ],
      "expansion": "∀ gr_product_index_gaussianfactorization. Lt(gr_product_index_gaussianfactorization,l) → GProductStep(b,c,h,e,gr_product_index_gaussianfactorization)",
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      "meaning": "Every index i<l has an actual Gaussian multiplication step in the same beta-coded cumulative history.",
      "milestone_users": [],
      "name": "GProductSteps",
      "parameters": [
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      "transitive_dependencies": [
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        "GProductStep",
        "Lt",
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        "SignedDecode",
        "ZPairRep"
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      "transitive_dependents": [
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    },
    {
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      "dependencies": [
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      "dependents": [
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        "GIrreducibleFactorization",
        "GPrime",
        "GPrimeFactorization",
        "GProperNormDivisor",
        "GStrictNonunitFactorization"
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      "expansion": "GDvd(z,6)",
      "expansion_sha256": "05a744ac3514714f40ed43bc7051783ff0aaf75cbaf6e957c16c167000171453",
      "meaning": "An actual Gaussian inverse multiplies z to canonical Gaussian identity code 6. Natural code 1 is not this identity.",
      "milestone_users": [],
      "name": "GUnit",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "reviewed_id": "ND0209",
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      "transitive_dependencies": [
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        "ZPairRep"
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      "transitive_dependents": [
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    },
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      "dependencies": [
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      "dependents": [
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      "expansion": "∃ ics_raw_positive_secondwave. ∃ ics_raw_positive_scale_secondwave. ∃ ics_raw_negative_secondwave. ∃ ics_raw_negative_scale_secondwave. SignedMatrixProduct(ab,ac,db,dc,eb,ec,fb,fc,w,1,r,ics_raw_positive_secondwave,ics_raw_positive_scale_secondwave,ics_raw_negative_secondwave,ics_raw_negative_scale_secondwave) ∧ IntegerVectorEqual(ics_raw_positive_secondwave,ics_raw_positive_scale_secondwave,ics_raw_negative_secondwave,ics_raw_negative_scale_secondwave,pb,pc,nb,nc,r)",
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      "meaning": "An actual coded signed matrix product of output width one, compared to the requested output by integer-vector equality.",
      "milestone_users": [
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      "name": "IntegerMatrixVectorProduct",
      "parameters": [
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        "reviewed_id": "ND0124",
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        "MatrixPointwiseAdd",
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    },
    {
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      "dependencies": [
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      "dependents": [
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      "expansion": "¬n = 1 ∧ (PerfectPowerProfileCode(w,pb,pc,eb,ec,vb,vc,l,g,rb,rc) ∧ (PrimeValuationSupport(n,pb,pc,eb,ec,vb,vc,l) ∧ (PrimeExponentPrefixGCD(eb,ec,l,g) ∧ (¬g = 0 ∧ PerfectPowerRootTable(n,g,rb,rc)))))",
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      "expansion": "BetaPrefixInto(ab,ac,L,p) ∧ (BetaPrefixInto(bb,bc,M,p) ∧ (PolynomialProductLength(L,M,N) ∧ FpConvolutionPrefix(p,ab,ac,L,bb,bc,M,cb,cc,N)))",
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      "meaning": "Canonical input prefixes, the proper product length, and a genuine convolution output prefix. Terms beyond this length vanish by a separate support theorem, not by assuming the discarded tail is zero.",
      "milestone_users": [],
      "name": "FpPolyProduct",
      "parameters": [
        "p",
        "ab",
        "ac",
        "L",
        "bb",
        "bc",
        "M",
        "cb",
        "cc",
        "N"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "FpPolyProduct",
        "blueprint_parameters": [
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          "L",
          "bb",
          "bc",
          "M",
          "cb",
          "cc",
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "b701caf810fdc5025b83b9efb9f96e81fbb49d6b9b8d6e814aae89693255fca7",
        "reviewed_id": "ND0297",
        "reviewed_name": "FpPolyProduct",
        "reviewed_parameters": [
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          "ac",
          "L",
          "bb",
          "bc",
          "M",
          "cb",
          "cc",
          "N"
        ],
        "route": "polynomial-products"
      },
      "topological_layer": 6,
      "transitive_dependencies": [
        "Beta",
        "BetaAt",
        "BetaPrefixInto",
        "BetaSum",
        "BetaZeroExtend",
        "CanonicalModularResidue",
        "FpConvolutionCoefficient",
        "FpConvolutionPrefix",
        "Le",
        "Lt",
        "Mod",
        "PolynomialDiagonalPrefix",
        "PolynomialDiagonalTerm",
        "PolynomialProductLength"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 8,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "FpHornerTrace",
        "MatrixAffineSlice"
      ],
      "dependents": [],
      "expansion": "∃ pfs_history_code_polynomial_division_definition. ∃ pfs_history_scale_polynomial_division_definition. FpHornerTrace(p,b,c,a,S n,r,pfs_history_code_polynomial_division_definition,pfs_history_scale_polynomial_division_definition) ∧ MatrixAffineSlice(pfs_history_code_polynomial_division_definition,pfs_history_scale_polynomial_division_definition,1,1,qb,qc,n)",
      "expansion_sha256": "6ebc718c00ffc163d5983aa9746c22836f6979d9d2614b4c822517e6c98e6dfc",
      "meaning": "An actual FpHornerTrace processes S n highest-degree-first coefficients at the canonical argument a and ends at r. An actual MatrixAffineSlice with offset 1 and stride 1 records n quotient coefficients from that same history; constants therefore have an empty quotient. The coefficient recurrence and division identity are not graph premises. This is not arbitrary-divisor Euclidean division or G091.",
      "milestone_users": [
        "G091"
      ],
      "name": "FpSyntheticDivision",
      "parameters": [
        "p",
        "b",
        "c",
        "a",
        "n",
        "qb",
        "qc",
        "r"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "FpSyntheticDivision",
        "blueprint_parameters": [
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "4726f77751694ac54385e152f67a5023bda4c8fef0fad661b545a488b423b178",
        "reviewed_id": "ND0333",
        "reviewed_name": "FpSyntheticDivision",
        "reviewed_parameters": [
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          "a",
          "n",
          "qb",
          "qc",
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        ],
        "route": "polynomial-division-prerequisites"
      },
      "topological_layer": 6,
      "transitive_dependencies": [
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        "BetaAt",
        "CanonicalModularResidue",
        "FpAdd",
        "FpHornerStep",
        "FpHornerSteps",
        "FpHornerTrace",
        "FpMul",
        "Lt",
        "MatrixAffineSlice",
        "Mod"
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    },
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "GMul",
        "GUnit"
      ],
      "dependents": [
        "GFactorAssociateMatching"
      ],
      "expansion": "∃ gr_unit_gaussianfactorization. GUnit(gr_unit_gaussianfactorization) ∧ GMul(gr_unit_gaussianfactorization,a,b)",
      "expansion_sha256": "7f57b3d1ad6f53251fc3c2d5e2e39064d6dda66db44f8220f883847b61d5b16c",
      "meaning": "A genuinely witnessed Gaussian unit u satisfies GMul(u,a,b). Associated factor codes need not be literally equal.",
      "milestone_users": [],
      "name": "GAssociate",
      "parameters": [
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        "b"
      ],
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        "reviewed_parameters": [
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        ],
        "route": "gaussian-factorization"
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      "topological_layer": 6,
      "transitive_dependencies": [
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        "GMul",
        "GUnit",
        "SignedBalance",
        "SignedDecode",
        "ZPairRep"
      ],
      "transitive_dependents": [
        "GFactorAssociateMatching",
        "GFactorPermutation",
        "GMatchedFactors"
      ]
    },
    {
      "arity": 1,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "GMul",
        "GUnit",
        "ZPairValid"
      ],
      "dependents": [
        "GAllIrreducible"
      ],
      "expansion": "ZPairValid(z) ∧ (¬z = 0 ∧ (¬GUnit(z) ∧ (∀ x. ∀ y. GMul(x,y,z) → GUnit(x) ∨ GUnit(y))))",
      "expansion_sha256": "f85b5e8985b52ba3a13cca36352fd469d5f7da6fbdbbe1e0994d5fda5229b038",
      "meaning": "A valid nonzero Gaussian nonunit whose every actual factorization has a unit factor. No prime-divisor property is assumed.",
      "milestone_users": [],
      "name": "GIrreducible",
      "parameters": [
        "z"
      ],
      "reviewed_incompatibility": null,
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        "blueprint_name": "GIrreducible",
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      "topological_layer": 6,
      "transitive_dependencies": [
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        "GMul",
        "GUnit",
        "SignedBalance",
        "SignedDecode",
        "ZPairDecode",
        "ZPairRep",
        "ZPairValid"
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      "transitive_dependents": [
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    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "GDvd",
        "GMul",
        "GUnit",
        "ZPairValid"
      ],
      "dependents": [
        "GAllPrime"
      ],
      "expansion": "ZPairValid(z) ∧ (¬z = 0 ∧ (¬GUnit(z) ∧ (∀ x. ∀ y. ∀ n. GMul(x,y,n) → GDvd(z,n) → GDvd(z,x) ∨ GDvd(z,y))))",
      "expansion_sha256": "0655509a0dbfe2e0673e522b2e7636222fcec19301006ca3403d248ed084432f",
      "meaning": "A valid nonzero Gaussian nonunit dividing an actual product only if it divides a factor. Equivalence with irreducibility is proved, not part of either definition.",
      "milestone_users": [],
      "name": "GPrime",
      "parameters": [
        "z"
      ],
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        "route": "gaussian-factorization"
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      "transitive_dependencies": [
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        "GMul",
        "GUnit",
        "SignedBalance",
        "SignedDecode",
        "ZPairDecode",
        "ZPairRep",
        "ZPairValid"
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      "transitive_dependents": [
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        "GPrimeFactorization"
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    },
    {
      "arity": 4,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "BetaAt",
        "GProductSteps"
      ],
      "dependents": [
        "GIrreducibleFactorization",
        "GPrimeFactorization"
      ],
      "expansion": "∃ gr_product_trace_gaussianfactorization. ∃ gr_product_scale_gaussianfactorization. BetaAt(gr_product_trace_gaussianfactorization,gr_product_scale_gaussianfactorization,0,6) ∧ (BetaAt(gr_product_trace_gaussianfactorization,gr_product_scale_gaussianfactorization,l,P) ∧ GProductSteps(b,c,gr_product_trace_gaussianfactorization,gr_product_scale_gaussianfactorization,l))",
      "expansion_sha256": "2c59774be7a870a41a03ccae5fdaf22c253ce57c21a7989146ac4eb0c10c9ba0",
      "meaning": "A real beta multiplication history begins at Gaussian identity code 6, performs the stated l factor steps, and ends at P. No prime or uniqueness conclusion is included.",
      "milestone_users": [],
      "name": "GProduct",
      "parameters": [
        "b",
        "c",
        "l",
        "P"
      ],
      "reviewed_incompatibility": null,
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        "reviewed_expansion_sha256": "c4b4b937824cf6c330756f2372665803bb427a1e1cd0fc37f8af76a6a4d1ec6e",
        "reviewed_id": "ND0220",
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        ],
        "route": "gaussian-factorization"
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      "topological_layer": 6,
      "transitive_dependencies": [
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        "GMul",
        "GProductStep",
        "GProductSteps",
        "Lt",
        "SignedBalance",
        "SignedDecode",
        "ZPairRep"
      ],
      "transitive_dependents": [
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        "GPrimeFactorization"
      ]
    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "GDvd",
        "GNorm",
        "GUnit",
        "Lt"
      ],
      "dependents": [],
      "expansion": "¬GUnit(d) ∧ (GDvd(d,z) ∧ (∃ x. GNorm(d,x) ∧ Lt(x,N)))",
      "expansion_sha256": "aabad16d6ebeafe1930128ed2f131bcd910f075669e695167efa1fecce14e1af",
      "meaning": "d is an actual nonunit divisor of z and has a witnessed actual Gaussian norm strictly below N. This is not a supplied factorization oracle.",
      "milestone_users": [],
      "name": "GProperNormDivisor",
      "parameters": [
        "d",
        "z",
        "N"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "GProperNormDivisor",
        "blueprint_parameters": [
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        "reviewed_expansion_sha256": "dd9e59e0a8b6ed4fe0ad1f95ace524c9803d9a8fbe6f5265c212224e9816b269",
        "reviewed_id": "ND0216",
        "reviewed_name": "GProperNormDivisor",
        "reviewed_parameters": [
          "d",
          "z",
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        ],
        "route": "gaussian-factorization"
      },
      "topological_layer": 6,
      "transitive_dependencies": [
        "GDvd",
        "GMul",
        "GNorm",
        "GUnit",
        "GaussianSignedNorm",
        "Lt",
        "SignedBalance",
        "SignedDecode",
        "SignedDifferenceSquare",
        "ZPairRep"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 6,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "GMul",
        "GNorm",
        "GUnit",
        "Lt"
      ],
      "dependents": [],
      "expansion": "GMul(a,b,z) ∧ (GNorm(a,A) ∧ (GNorm(b,B) ∧ (¬GUnit(a) ∧ (¬GUnit(b) ∧ (Lt(A,N) ∧ Lt(B,N))))))",
      "expansion_sha256": "fb51c8ae0bd1b455871b46e1c19c68f014fca02eb4dc3c1aaecf5b2fe333e1ca",
      "meaning": "An actual Gaussian product a*b=z, two actual factor norms A,B, nonunit factors, and both strict norm bounds below N. Its existence is a proved search outcome.",
      "milestone_users": [],
      "name": "GStrictNonunitFactorization",
      "parameters": [
        "z",
        "N",
        "a",
        "b",
        "A",
        "B"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "GStrictNonunitFactorization",
        "blueprint_parameters": [
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          "a",
          "b",
          "A",
          "B"
        ],
        "kind": "exact-name",
        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "808b8e4507ffc7a829d69833ff43534f17385a133b1b2ea54ef8835b5987d0a9",
        "reviewed_id": "ND0217",
        "reviewed_name": "GStrictNonunitFactorization",
        "reviewed_parameters": [
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          "N",
          "a",
          "b",
          "A",
          "B"
        ],
        "route": "gaussian-factorization"
      },
      "topological_layer": 6,
      "transitive_dependencies": [
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        "GMul",
        "GNorm",
        "GUnit",
        "GaussianSignedNorm",
        "Lt",
        "SignedBalance",
        "SignedDecode",
        "SignedDifferenceSquare",
        "ZPairRep"
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      "transitive_dependents": []
    },
    {
      "arity": 10,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "IntegerMatrixVectorProduct"
      ],
      "dependents": [],
      "expansion": "∃ ics_coefficient_positive_secondwave. ∃ ics_coefficient_positive_scale_secondwave. ∃ ics_coefficient_negative_secondwave. ∃ ics_coefficient_negative_scale_secondwave. IntegerMatrixVectorProduct(ab,ac,db,dc,ics_coefficient_positive_secondwave,ics_coefficient_positive_scale_secondwave,ics_coefficient_negative_secondwave,ics_coefficient_negative_scale_secondwave,w,r,pb,pc,nb,nc)",
      "expansion_sha256": "cf4c2d6e13f2f0e4aa97c423de3ad6d9103974d2c9a98501e69719048a9305ed",
      "meaning": "Actual finite signed coefficient codes witness the output as an integer linear combination of the matrix columns; no independence, index, or covolume is assumed.",
      "milestone_users": [
        "T13"
      ],
      "name": "IntegerColumnSpan",
      "parameters": [
        "ab",
        "ac",
        "db",
        "dc",
        "w",
        "r",
        "pb",
        "pc",
        "nb",
        "nc"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": {
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        "blueprint_name": "IntegerColumnSpan",
        "blueprint_parameters": [
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          "w",
          "r",
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        "reviewed_expansion_sha256": "b0af6f5cad6c1442c2b38424fc85ee7c8d55508206430c94f3366be554af4afc",
        "reviewed_id": "ND0125",
        "reviewed_name": "IntegerColumnSpan",
        "reviewed_parameters": [
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          "w",
          "r",
          "pb",
          "pc",
          "nb",
          "nc"
        ],
        "route": "integer-linear-algebra"
      },
      "topological_layer": 6,
      "transitive_dependencies": [
        "Beta",
        "BetaAt",
        "DotProduct",
        "IntegerMatrixVectorProduct",
        "IntegerVectorEqual",
        "Lt",
        "MatrixAffineSlice",
        "MatrixPointwiseAdd",
        "MatrixProductCell",
        "MatrixProductPrefix",
        "SignedMatrixProduct"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 2,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "PerfectPowerProfileData",
        "Pow"
      ],
      "dependents": [],
      "expansion": "n = 1 ∧ (w = 0 ∧ (∀ x. ¬x = 0 → Pow(1,x,1))) ∨ (∃ x. ∃ y. ∃ z. ∃ m. ∃ k. ∃ i. ∃ j. ∃ u. ∃ v. ∃ x0. PerfectPowerProfileData(n,w,x,y,z,m,k,i,j,u,v,x0))",
      "expansion_sha256": "c71f7d51436b34ddce00cb9caf267f5aaf652de60a766d310861d36a2b2efae8",
      "meaning": "Either n=1 with code zero and a uniform proof of every positive unit power, or the actual finite nonunit prime-valuation and root profile. Zero is excluded.",
      "milestone_users": [
        "G010"
      ],
      "name": "PowerProfile",
      "parameters": [
        "n",
        "w"
      ],
      "reviewed_incompatibility": null,
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        "blueprint_name": "PowerProfile",
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_expansion_sha256": "5d06d1438c736f85220832be118c540c2aefe6612ca91016cebbf040e10769f0",
        "reviewed_id": "ND0195",
        "reviewed_name": "PowerProfile",
        "reviewed_parameters": [
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          "w"
        ],
        "route": "squarefree-kernels"
      },
      "topological_layer": 6,
      "transitive_dependencies": [
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        "BoundedPowerValuation",
        "Dvd",
        "InjectivePrefix",
        "Le",
        "Lt",
        "NaturalPair",
        "PerfectPowerProfileCode",
        "PerfectPowerProfileData",
        "PerfectPowerRootTable",
        "Pow",
        "PowerDivides",
        "Prime",
        "PrimeDivisorSupport",
        "PrimeExponentEntries",
        "PrimeExponentPrefixGCD",
        "PrimeValuationSupport",
        "Product"
      ],
      "transitive_dependents": []
    },
    {
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      "authority": "blueprint-vocabulary-only",
      "dependencies": [
        "Order",
        "Phi"
      ],
      "dependents": [],
      "expansion": "∃ t. Phi(m,t) ∧ Order(g,(Z/mZ)*,t)",
      "expansion_sha256": "c9032dc0020d4e1080e7fdee097479e8aa27509e883f55e88996996008207235",
      "meaning": "Generator of all modular units.",
      "milestone_users": [
        "G017",
        "G018",
        "G019"
      ],
      "name": "PrimitiveRoot",
      "parameters": [
        "g",
        "m"
      ],
      "reviewed_incompatibility": null,
      "reviewed_match": null,
      "topological_layer": 6,
      "transitive_dependencies": [
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        "BetaAt",
        "BetaSum",
        "Coprime",
        "Dvd",
        "Gcd",
        "Lt",
        "Order",
        "Phi",
        "UnitBitPrefix",
        "UnitCount"
      ],
      "transitive_dependents": []
    },
    {
      "arity": 8,
      "authority": "blueprint-vocabulary-only",
      "dependencies": [
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        "Lt",
        "SignedMinorRecord"
      ],
      "dependents": [],
      "expansion": "∀j. Lt(j,l) → ∃z. Beta(b,c,j,z) ∧ SignedMinorRecord(pb,pc,nb,nc,q,j,z)",
      "expansion_sha256": "e48d73419574f2e9040d44c8085e230aad6954cad29e9928f1418ff6dcd18f38",
      "meaning": "A complete beta-coded finite prefix of exact injectively packed first-row signed cofactor minors.",
      "milestone_users": [],
      "name": "SignedCofactorMinorPrefix",
      "parameters": [
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        "pc",
        "nb",
        "nc",
        "q",
        "b",
        "c",
        "l"
      ],
      "reviewed_incompatibility": null,
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        "blueprint_name": "SignedCofactorMinorPrefix",
        "blueprint_parameters": [
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          "pc",
          "nb",
          "nc",
          "q",
          "b",
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        "reviewed_argument_blueprint_positions": [
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        "reviewed_id": "ND0060",
        "reviewed_name": "SignedCofactorMinorPrefix",
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          "q",
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        "route": "matrix-cofactor-expansion"
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      "expansion": "d = 0 ∧ (p = 1 ∧ n = 0) ∨ (∃ x. ∃ y. ∃ z. ∃ m. ∃ k. d = S x ∧ (SignedDeterminantChildPrefix(b,c,i,pb,pc,nb,nc,x,y,z,m,k,S x) ∧ SignedAlternatingCofactorFold(pb,pc,nb,nc,y,z,m,k,S x,p,n)))",
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      "transitive_dependents": [
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      "expansion": "∃ di_delta_dirichlet_inverse. KroneckerDeltaTable(N,di_delta_dirichlet_inverse) ∧ (DirichletTable(N,F,G,di_delta_dirichlet_inverse) ∧ DirichletTable(N,G,F,di_delta_dirichlet_inverse))",
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      "meaning": "Witness a real Kronecker delta table E and both actual convolution tables F*G=E and G*F=E on 0<n<=N. Their graphs include actual table validity; values at zero remain unrestricted. The unit-at-one criterion is not a definition premise, and its necessity requires N>0; zero-window inverse identities are separately proved for all actual input tables.",
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      "expansion": "FpOperationTables(p,ab,ac,mb,mc,nb,nc,ib,ic) ∧ (FpCardinality(p,eb,ec) ∧ (FpFieldLaws(p) ∧ FpCharacteristic(p)))",
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      "meaning": "The constructed prime-order structure combines actual operation tables, a p-element bijection, proved field laws and exact characteristic. Its existence is a theorem; extension fields of order p^k remain a separate open goal.",
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      "expansion": "∀ gr_factor_index_gaussianfactorization. ∀ gr_factor_value_gaussianfactorization. Lt(gr_factor_index_gaussianfactorization,l) → BetaAt(b,c,gr_factor_index_gaussianfactorization,gr_factor_value_gaussianfactorization) → GIrreducible(gr_factor_value_gaussianfactorization)",
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      "meaning": "Every actual decoded entry of the finite beta prefix is a Gaussian irreducible; repeated or associated factors remain distinct occurrences.",
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      "dependencies": [
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      "dependents": [
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      "expansion": "∀ gr_prime_factor_index_gaussianfactorization. ∀ gr_prime_factor_value_gaussianfactorization. Lt(gr_prime_factor_index_gaussianfactorization,l) → BetaAt(b,c,gr_prime_factor_index_gaussianfactorization,gr_prime_factor_value_gaussianfactorization) → GPrime(gr_prime_factor_value_gaussianfactorization)",
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      "meaning": "Every actual decoded entry of the finite prefix satisfies the full Gaussian prime-divisor graph.",
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      "expansion": "∀ gr_match_index_gaussianfactorization. ∀ gr_match_image_gaussianfactorization. ∀ gr_match_source_gaussianfactorization. ∀ gr_match_target_gaussianfactorization. Lt(gr_match_index_gaussianfactorization,l) → BetaAt(u,v,gr_match_index_gaussianfactorization,gr_match_image_gaussianfactorization) → BetaAt(b,c,gr_match_index_gaussianfactorization,gr_match_source_gaussianfactorization) → BetaAt(d,e,gr_match_image_gaussianfactorization,gr_match_target_gaussianfactorization) → GAssociate(gr_match_source_gaussianfactorization,gr_match_target_gaussianfactorization)",
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      "meaning": "Every actual decoded source factor and its decoded image factor are related by an actual multiplicative unit witness. This graph alone does not assert that the map is bijective.",
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      "expansion": "∀ mdr_i_secondwave. Lt(mdr_i_secondwave,l) → ∃ x. ∃ y. ∃ z. ∃ n. ∃ m. ∃ k. ∃ i. SignedDeterminantNodeAt(b,c,mdr_i_secondwave,x,y,z,n,m,k,i) ∧ SignedDeterminantLocalStep(b,c,mdr_i_secondwave,x,y,z,n,m,k,i)",
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      "milestone_users": [
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      "name": "SignedDeterminantHistory",
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      "expansion": "GUnit(u) ∧ (GAllIrreducible(b,c,l) ∧ (∃ x. GProduct(b,c,l,x) ∧ GMul(u,x,z)))",
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        "route": "gaussian-factorization"
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      "dependencies": [
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      "dependents": [
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      "expansion": "PermutationPrefix(u,v,l) ∧ GFactorAssociateMatching(b,c,d,e,u,v,l)",
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      "meaning": "An actual bounded, injective, surjective beta index map matches all source and target factor occurrences by witnessed Gaussian units.",
      "milestone_users": [
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      "name": "GMatchedFactors",
      "parameters": [
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        "d",
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        "v",
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      "topological_layer": 8,
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        "GFactorAssociateMatching",
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        "GUnit",
        "InjectivePrefix",
        "Lt",
        "PermutationPrefix",
        "SignedBalance",
        "SignedDecode",
        "SurjectivePrefix",
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    },
    {
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      "dependencies": [
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        "GMul",
        "GProduct",
        "GUnit"
      ],
      "dependents": [],
      "expansion": "GUnit(u) ∧ (GAllPrime(b,c,l) ∧ (∃ x. GProduct(b,c,l,x) ∧ GMul(u,x,z)))",
      "expansion_sha256": "9cb481ac95f326102e5f0ac84dff4f0e53a4de23b2f1de548599b8b56c9f4600",
      "meaning": "An actual unit and actual finite RingPrime Gaussian factor list reconstruct z through a genuine multiplication trace. Zero is excluded by theorem, not a hidden extra premise here.",
      "milestone_users": [
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      ],
      "name": "GPrimeFactorization",
      "parameters": [
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      "reviewed_incompatibility": null,
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        "ZPairRep",
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      "dependencies": [
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        "SignedDeterminantNodeAt"
      ],
      "dependents": [
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        "SignedEvaluatedCofactors",
        "SignedSelectedDeterminant"
      ],
      "expansion": "∃ mdr_b_secondwave. ∃ mdr_c_secondwave. ∃ mdr_l_secondwave. ∃ mdr_i_secondwave. SignedDeterminantHistory(mdr_b_secondwave,mdr_c_secondwave,mdr_l_secondwave) ∧ (Lt(mdr_i_secondwave,mdr_l_secondwave) ∧ SignedDeterminantNodeAt(mdr_b_secondwave,mdr_c_secondwave,mdr_i_secondwave,d,pb,pc,nb,nc,p,n))",
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      "meaning": "An actual evaluating root in a finite cofactor DAG for an arbitrary-dimensional signed matrix; its mathematical value is p−n.",
      "milestone_users": [
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      "name": "SignedRecursiveDeterminant",
      "parameters": [
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        "pc",
        "nb",
        "nc",
        "d",
        "p",
        "n"
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        "MatrixSkipIndex",
        "Odd",
        "SignedAlternatingCofactorFold",
        "SignedAlternatingCofactorTerm",
        "SignedAlternatingProductPrefix",
        "SignedDeterminantChildPrefix",
        "SignedDeterminantHistory",
        "SignedDeterminantLocalStep",
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      "expansion": "∃ mdr_p_secondwave. ∃ mdr_n_secondwave. SignedRecursiveDeterminant(ab,ac,bb,bc,d,mdr_p_secondwave,mdr_n_secondwave) ∧ (mdr_p_secondwave = mdr_n_secondwave + D ∨ mdr_n_secondwave = mdr_p_secondwave + D)",
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        "SignedAlternatingCofactorFold",
        "SignedAlternatingCofactorTerm",
        "SignedAlternatingProductPrefix",
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      "dependencies": [
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      "expansion": "l = m ∧ GMatchedFactors(b,c,d,e,u,v,l)",
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      "meaning": "The two actual lengths are equal and the given beta map is a genuine unit-matching finite permutation. No identical factor-code or leading-unit claim is made.",
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      "name": "GFactorPermutation",
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      "expansion": "∀ mdr_j_secondwave. Lt(mdr_j_secondwave,S q) → ∃ x. ∃ y. ∃ z. ∃ n. ∃ m. ∃ k. SignedMatrixMinor(pb,pc,nb,nc,S q,0,mdr_j_secondwave,q,x,y,z,n) ∧ (SignedRecursiveDeterminant(x,y,z,n,q,m,k) ∧ (Beta(eb,ec,mdr_j_secondwave,m) ∧ Beta(fb,fc,mdr_j_secondwave,k)))",
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      "meaning": "Actual determinants of every genuine first-row minor are stored in the cofactor streams, not assumed as unrelated values.",
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        "fc"
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      "dependencies": [
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      "expansion": "∃ mdr_ub_secondwave. ∃ mdr_uc_secondwave. ∃ mdr_vb_secondwave. ∃ mdr_vc_secondwave. SignedSelectedSubmatrix(pb,pc,nb,nc,w,rb,rc,cb,cc,q,mdr_ub_secondwave,mdr_uc_secondwave,mdr_vb_secondwave,mdr_vc_secondwave) ∧ SignedRecursiveDeterminant(mdr_ub_secondwave,mdr_uc_secondwave,mdr_vb_secondwave,mdr_vc_secondwave,q,p,n)",
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      "meaning": "An actual selected submatrix and its unrestricted recursive determinant, not a supplied table of purported minor values.",
      "milestone_users": [
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        "pc",
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        "rb",
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        "cb",
        "cc",
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      "expansion": "∀ mdr_rb_secondwave. ∀ mdr_rc_secondwave. ∀ mdr_cb_secondwave. ∀ mdr_cc_secondwave. ∀ mdr_p_secondwave. ∀ mdr_n_secondwave. FiniteMatrixSelector(mdr_rb_secondwave,mdr_rc_secondwave,q,r) → FiniteMatrixSelector(mdr_cb_secondwave,mdr_cc_secondwave,q,w) → SignedSelectedDeterminant(pb,pc,nb,nc,w,mdr_rb_secondwave,mdr_rc_secondwave,mdr_cb_secondwave,mdr_cc_secondwave,q,mdr_p_secondwave,mdr_n_secondwave) → mdr_p_secondwave = mdr_n_secondwave",
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      "source": "T06",
      "target": "DivRem"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T07",
      "target": "Gcd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T08",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T09",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T09",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T10",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T10",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T11",
      "target": "Prod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T11",
      "target": "Seq"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T11",
      "target": "Sum"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T12",
      "target": "Horner"
    },
    {
      "kind": "declared_notation",
      "source": "T12",
      "target": "Horner"
    },
    {
      "kind": "declared_notation",
      "source": "T12",
      "target": "Beta"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T13",
      "target": "RectangularMatrixRank"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedDeterminantNodeCode"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "BetaAt"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedDeterminantNodeAt"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "Le"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixSkipIndex"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "Beta"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixMinorCell"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixMinorPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedMatrixMinor"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedDeterminantChildPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "Even"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "Odd"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedAlternatingCofactorTerm"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedAlternatingProductPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "BetaSum"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedAlternatingCofactorFold"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedDeterminantLocalStep"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedDeterminantHistory"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedRecursiveDeterminant"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedEvaluatedCofactors"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedMatrixPrefixEquality"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "UniformBetaPrefixBox"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "FiniteMatrixSelector"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedSelectedSubmatrix"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedSelectedDeterminant"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "NonzeroSelectedMinor"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "NonzeroMatrixMinor"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "AllSignedMinorsZero"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "RectangularMatrixRank"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerVectorEqual"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerVectorZero"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerVectorAdd"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerVectorNegate"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixAffineSlice"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "DotProduct"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixProductCell"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixProductPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "MatrixPointwiseAdd"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "SignedMatrixProduct"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerMatrixVectorProduct"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerColumnSpan"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IntegerMatrixEntrywiseEqual"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "AbsoluteRecursiveDeterminant"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "PositiveDeterminantMatrixData"
    },
    {
      "kind": "declared_notation",
      "source": "T13",
      "target": "IdentityMatrixSelector"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T14",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T14",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T16",
      "target": "At"
    },
    {
      "kind": "statement_uses_definition",
      "source": "T16",
      "target": "Seq"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A01",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A01",
      "target": "QuadBit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A02",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A03",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A03",
      "target": "QuadBit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A04",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A04",
      "target": "CarryCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A04",
      "target": "PowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A04",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A05",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A05",
      "target": "PowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A05",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A05",
      "target": "Rep2"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A06",
      "target": "Rep4"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A07",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A07",
      "target": "Digits"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A07",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A07",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A08",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "A08",
      "target": "PrimitiveTriple"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G001",
      "target": "DivRem"
    },
    {
      "kind": "declared_notation",
      "source": "G001",
      "target": "DivRem"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G002",
      "target": "IsGCD"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G002",
      "target": "SignedBezout"
    },
    {
      "kind": "declared_notation",
      "source": "G002",
      "target": "SignedBezout"
    },
    {
      "kind": "declared_notation",
      "source": "G002",
      "target": "IsGCD"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G003",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G003",
      "target": "Dvd"
    },
    {
      "kind": "declared_notation",
      "source": "G003",
      "target": "Dvd"
    },
    {
      "kind": "declared_notation",
      "source": "G003",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G004",
      "target": "PrimeFactorList"
    },
    {
      "kind": "declared_notation",
      "source": "G004",
      "target": "PrimeFactorList"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G005",
      "target": "PrimeFactorList"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G005",
      "target": "PrimeFactorListPermutation"
    },
    {
      "kind": "declared_notation",
      "source": "G005",
      "target": "PrimeFactorList"
    },
    {
      "kind": "declared_notation",
      "source": "G005",
      "target": "PrimeFactorListPermutation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G006",
      "target": "EulerProduct"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G006",
      "target": "Phi"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G006",
      "target": "PrimeFactorList"
    },
    {
      "kind": "declared_notation",
      "source": "G006",
      "target": "Phi"
    },
    {
      "kind": "declared_notation",
      "source": "G006",
      "target": "EulerProduct"
    },
    {
      "kind": "declared_notation",
      "source": "G006",
      "target": "PrimeFactorList"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G007",
      "target": "ArithPositiveEqual"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G007",
      "target": "ArithTable"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G007",
      "target": "DirichletTable"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G007",
      "target": "DivisorTransform"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G007",
      "target": "MobiusTable"
    },
    {
      "kind": "declared_notation",
      "source": "G007",
      "target": "ArithTable"
    },
    {
      "kind": "declared_notation",
      "source": "G007",
      "target": "MobiusTable"
    },
    {
      "kind": "declared_notation",
      "source": "G007",
      "target": "ArithPositiveEqual"
    },
    {
      "kind": "declared_notation",
      "source": "G007",
      "target": "DirichletTable"
    },
    {
      "kind": "declared_notation",
      "source": "G007",
      "target": "DivisorTransform"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G008",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G008",
      "target": "Jordan"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G009",
      "target": "ArithPositiveEqual"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G009",
      "target": "DirichletTable"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G009",
      "target": "MultiplicativePrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G009",
      "target": "ArithPositiveEqual"
    },
    {
      "kind": "declared_notation",
      "source": "G009",
      "target": "DirichletTable"
    },
    {
      "kind": "declared_notation",
      "source": "G009",
      "target": "MultiplicativePrefix"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G010",
      "target": "PowerProfile"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G010",
      "target": "Squarefree"
    },
    {
      "kind": "declared_notation",
      "source": "G010",
      "target": "Squarefree"
    },
    {
      "kind": "declared_notation",
      "source": "G010",
      "target": "PowerProfile"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G011",
      "target": "CRTNormalizedPrefixSolution"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G011",
      "target": "CRTPairwiseCompatiblePrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "BetaAt"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "Dvd"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "IsGCD"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "ModEq"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "CRTPrefixGcdCongruences"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "Beta"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "CRTPrefixLCM"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "CRTPrefixSolution"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "CRTNormalizedPrefixSolution"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "CRTPairwiseCompatiblePrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "CRTPositiveModuliPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G011",
      "target": "Le"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G012",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G012",
      "target": "Gcd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G012",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G013",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G013",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G014",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G014",
      "target": "ModEq"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G014",
      "target": "Phi"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G014",
      "target": "Pow"
    },
    {
      "kind": "declared_notation",
      "source": "G014",
      "target": "Coprime"
    },
    {
      "kind": "declared_notation",
      "source": "G014",
      "target": "ModEq"
    },
    {
      "kind": "declared_notation",
      "source": "G014",
      "target": "Pow"
    },
    {
      "kind": "declared_notation",
      "source": "G014",
      "target": "Phi"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G015",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G015",
      "target": "Order"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G015",
      "target": "Phi"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G015",
      "target": "Unit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G016",
      "target": "Carmichael"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G016",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G016",
      "target": "Unit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G017",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G017",
      "target": "PrimitiveRoot"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G018",
      "target": "PrimitiveRoot"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G018",
      "target": "PrimitiveRootModulus"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G019",
      "target": "Gcd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G019",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G019",
      "target": "Phi"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G019",
      "target": "PrimitiveRoot"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G019",
      "target": "Unit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G020",
      "target": "CRTSolution"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G020",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G021",
      "target": "Lt"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G021",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G021",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G021",
      "target": "Lt"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G022",
      "target": "BetaAt"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G022",
      "target": "InitialPrimeList"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G022",
      "target": "Lt"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G022",
      "target": "PowTwo"
    },
    {
      "kind": "declared_notation",
      "source": "G022",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G022",
      "target": "BetaAt"
    },
    {
      "kind": "declared_notation",
      "source": "G022",
      "target": "InitialPrimeList"
    },
    {
      "kind": "declared_notation",
      "source": "G022",
      "target": "PowTwo"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G023",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G023",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G023",
      "target": "Val"
    },
    {
      "kind": "declared_notation",
      "source": "G023",
      "target": "BertrandWindow"
    },
    {
      "kind": "declared_notation",
      "source": "G023",
      "target": "PowerValuationOne"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G024",
      "target": "At"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G024",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G024",
      "target": "Seq"
    },
    {
      "kind": "declared_notation",
      "source": "G024",
      "target": "BertrandChain"
    },
    {
      "kind": "declared_notation",
      "source": "G024",
      "target": "BertrandWindow"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G025",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G025",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G025",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G025",
      "target": "Mod4Three"
    },
    {
      "kind": "declared_notation",
      "source": "G025",
      "target": "Dvd"
    },
    {
      "kind": "declared_notation",
      "source": "G025",
      "target": "PrimeThreeModFourDivisor"
    },
    {
      "kind": "declared_notation",
      "source": "G025",
      "target": "EuclidThreeNumber"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G026",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G026",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G027",
      "target": "BitLen"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G027",
      "target": "Le"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G027",
      "target": "Lt"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G027",
      "target": "PrimeCount"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "BetaAt"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "PrimeBitPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "BetaSum"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "PrimeCount"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Le"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "BetaCutoffPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Product"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Repeat"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Pow"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "PowTwo"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "BitLen"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Primorial"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "Choose"
    },
    {
      "kind": "declared_notation",
      "source": "G027",
      "target": "CentralBinom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G028",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G028",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G028",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G029",
      "target": "LogBracket"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G029",
      "target": "PrimeCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G030",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G030",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G030",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G031",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G032",
      "target": "FactorialValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G032",
      "target": "LegendreSum"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G032",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G033",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G033",
      "target": "Digits"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G033",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G033",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G034",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G034",
      "target": "CarryCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G034",
      "target": "PowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G034",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G035",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G035",
      "target": "CarryCountMany"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G035",
      "target": "Multinomial"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G035",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BetaAt"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BetaSumTrace"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Le"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Dvd"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Product"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Repeat"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Pow"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "PowerDivides"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "PowerValuation"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BetaValuationPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Choose"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "MultinomialBinomialPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Multinomial"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BinaryAddCarryPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "DivRem"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "PowerQuotPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BetaSum"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "AllBits"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BitCount"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "BinaryColumnCarryCount"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "MultinomialCarryPrefix"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "CarryCountMany"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G035",
      "target": "PrimePowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G036",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G036",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G036",
      "target": "LiftedPowerDifference"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G036",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G036",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G036",
      "target": "Dvd"
    },
    {
      "kind": "declared_notation",
      "source": "G036",
      "target": "BoundedPowerValuation"
    },
    {
      "kind": "declared_notation",
      "source": "G036",
      "target": "LiftedPowerDifference"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G037",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G037",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G037",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G038",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G038",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G038",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G038",
      "target": "Val"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G039",
      "target": "Binom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G039",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G039",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G039",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G039",
      "target": "Val"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G040",
      "target": "CarryCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G040",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G040",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G040",
      "target": "Multinom"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G040",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G040",
      "target": "Val"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G041",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G041",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G041",
      "target": "Pow"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G041",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G042",
      "target": "Dvd"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G042",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G042",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G043",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G043",
      "target": "QuadBit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G044",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G044",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G044",
      "target": "QuadBit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G045",
      "target": "Coprime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G045",
      "target": "JacobiBit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G045",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G046",
      "target": "HilbertBit"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G046",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G047",
      "target": "Eisenstein"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G047",
      "target": "PowerSymbol"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G047",
      "target": "Primary"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G047",
      "target": "RingPrime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G048",
      "target": "Gaussian"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G048",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G048",
      "target": "PowerSymbol"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G049",
      "target": "HilbertProduct"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G050",
      "target": "PowerReciprocity"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G050",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G051",
      "target": "BitCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G051",
      "target": "CauchyDavenportBound"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G051",
      "target": "ModularSetSum"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G051",
      "target": "Prime"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "Lt"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "BetaAt"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetMember"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetSubset"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetUnion"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetIntersection"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModEq"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetPullback"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetSumCover"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularSetSum"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularTranslationBoundary"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "ModularDysonTransform"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "Le"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "CauchyDavenportBound"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "BetaSum"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "AllBits"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "BitCount"
    },
    {
      "kind": "declared_notation",
      "source": "G051",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G052",
      "target": "Seq"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G052",
      "target": "ZeroSubsequence"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G053",
      "target": "FiniteSet"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G053",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G053",
      "target": "RestrictedSum"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G054",
      "target": "FiniteSet"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G054",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G054",
      "target": "ZeroSubsequence"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G056",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G056",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G058",
      "target": "ArithmeticProgression"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G058",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G059",
      "target": "ArithmeticProgression"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G060",
      "target": "CapSet"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G060",
      "target": "CoefficientBound"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G061",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G061",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G061",
      "target": "Rep2"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G062",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G062",
      "target": "PowerValuation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G062",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G062",
      "target": "Rep2"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G063",
      "target": "RepCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G064",
      "target": "Rep4"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G065",
      "target": "RepCount"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G066",
      "target": "Rep3"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G067",
      "target": "Tri"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G068",
      "target": "PositiveDefinite"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G069",
      "target": "LocalRepresentation"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G069",
      "target": "QuadForm"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G069",
      "target": "ThreeSquareClass"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G070",
      "target": "ClassicallyIntegral"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G070",
      "target": "FifteenTest"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G070",
      "target": "PositiveDefinite"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G070",
      "target": "QuadForm"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G071",
      "target": "ContinuedFraction"
    },
    {
      "kind": "declared_notation",
      "source": "G071",
      "target": "ContinuedFraction"
    },
    {
      "kind": "declared_notation",
      "source": "G071",
      "target": "Beta"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G072",
      "target": "BestApproximationSecondKind"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G072",
      "target": "ContinuedFraction"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G072",
      "target": "Convergent"
    },
    {
      "kind": "declared_notation",
      "source": "G072",
      "target": "Convergent"
    },
    {
      "kind": "declared_notation",
      "source": "G072",
      "target": "BestApproximationSecondKind"
    },
    {
      "kind": "declared_notation",
      "source": "G072",
      "target": "ContinuedFraction"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G073",
      "target": "QuadraticPeriod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G075",
      "target": "QuadraticPeriod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G077",
      "target": "EuclidParametrization"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G077",
      "target": "PrimitiveTriple"
    },
    {
      "kind": "declared_notation",
      "source": "G077",
      "target": "PrimitiveTriple"
    },
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      "kind": "declared_notation",
      "source": "G077",
      "target": "EuclidParametrization"
    },
    {
      "kind": "declared_notation",
      "source": "G077",
      "target": "EuclidParameters"
    },
    {
      "kind": "declared_notation",
      "source": "G077",
      "target": "OppositeParity"
    },
    {
      "kind": "declared_notation",
      "source": "G078",
      "target": "FermatFourCounterexample"
    },
    {
      "kind": "declared_notation",
      "source": "G078",
      "target": "PrimitiveFermatFourCounterexample"
    },
    {
      "kind": "declared_notation",
      "source": "G078",
      "target": "SmallerFermatFourCounterexample"
    },
    {
      "kind": "declared_notation",
      "source": "G078",
      "target": "FermatFourStrictDescent"
    },
    {
      "kind": "declared_notation",
      "source": "G078",
      "target": "TrivialFermatFourSolution"
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    {
      "kind": "statement_uses_definition",
      "source": "G081",
      "target": "GEuclideanDivision"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G081",
      "target": "ZPairValid"
    },
    {
      "kind": "declared_notation",
      "source": "G081",
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    },
    {
      "kind": "declared_notation",
      "source": "G081",
      "target": "GEuclideanDivision"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G082",
      "target": "GMatchedFactors"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G082",
      "target": "GPrimeFactorization"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G082",
      "target": "ZPairValid"
    },
    {
      "kind": "declared_notation",
      "source": "G082",
      "target": "ZPairValid"
    },
    {
      "kind": "declared_notation",
      "source": "G082",
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    },
    {
      "kind": "declared_notation",
      "source": "G082",
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    },
    {
      "kind": "statement_uses_definition",
      "source": "G083",
      "target": "GNorm"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G083",
      "target": "Gaussian"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G083",
      "target": "Mod"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G083",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G083",
      "target": "RingPrime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G084",
      "target": "EEuclideanDivision"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G084",
      "target": "ZPairValid"
    },
    {
      "kind": "declared_notation",
      "source": "G084",
      "target": "EEuclideanDivision"
    },
    {
      "kind": "declared_notation",
      "source": "G084",
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    },
    {
      "kind": "statement_uses_definition",
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      "target": "Eisenstein"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G085",
      "target": "RingPrime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G086",
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    },
    {
      "kind": "statement_uses_definition",
      "source": "G086",
      "target": "Eisenstein"
    },
    {
      "kind": "statement_uses_definition",
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    {
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    {
      "kind": "statement_uses_definition",
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      "kind": "statement_uses_definition",
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    {
      "kind": "statement_uses_definition",
      "source": "G088",
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    },
    {
      "kind": "statement_uses_definition",
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    },
    {
      "kind": "statement_uses_definition",
      "source": "G089",
      "target": "Eval"
    },
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      "kind": "statement_uses_definition",
      "source": "G089",
      "target": "Prime"
    },
    {
      "kind": "statement_uses_definition",
      "source": "G090",
      "target": "RegularPrime"
    },
    {
      "kind": "statement_uses_definition",
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      "target": "FiniteField"
    },
    {
      "kind": "statement_uses_definition",
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      "target": "Irred"
    },
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      "target": "Prime"
    },
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      "target": "FpCoefficientNegation"
    },
    {
      "kind": "declared_notation",
      "source": "G091",
      "target": "FpCoefficientSubtraction"
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      "kind": "declared_notation",
      "source": "G091",
      "target": "PolynomialSuffix"
    },
    {
      "kind": "declared_notation",
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      "target": "FpPolynomialTrim"
    },
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      "kind": "declared_notation",
      "source": "G091",
      "target": "FpMonic"
    },
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      "target": "FpSyntheticDivision"
    },
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    {
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    },
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      "kind": "declared_notation",
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      "target": "Dvd"
    },
    {
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      "target": "Coprime"
    },
    {
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      "target": "SimpleHornerRoot"
    },
    {
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    },
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      "target": "BetaAt"
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    {
      "kind": "declared_notation",
      "source": "G095",
      "target": "SignedHornerValueDerivative"
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    {
      "kind": "declared_notation",
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      "target": "SignedDerivativeUnit"
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      "kind": "declared_notation",
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    },
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      "kind": "declared_notation",
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    },
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    {
      "kind": "declared_notation",
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      "target": "SignedDerivativeNonzero"
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    {
      "kind": "declared_notation",
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      "kind": "declared_notation",
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    },
    {
      "kind": "declared_notation",
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      "target": "Repeat"
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    {
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    {
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    {
      "kind": "statement_uses_definition",
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      "kind": "statement_uses_definition",
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    {
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    {
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    {
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      "kind": "declared_notation",
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    {
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    {
      "kind": "declared_notation",
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    {
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      "kind": "statement_uses_definition",
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      "target": "PrattCertificate"
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      "source": "G103",
      "target": "Prime"
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    {
      "kind": "statement_uses_definition",
      "source": "G104",
      "target": "PocklingtonCertificate"
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    {
      "kind": "statement_uses_definition",
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      "target": "Prime"
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      "kind": "statement_uses_definition",
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      "target": "Prime"
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      "target": "CornacchiaTrace"
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      "target": "Prime"
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    {
      "kind": "declared_notation",
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      "target": "Dvd"
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    {
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    {
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    {
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    {
      "kind": "declared_notation",
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      "target": "CornacchiaStateInvariant"
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    {
      "kind": "statement_uses_definition",
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    {
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      "target": "LLLReduced"
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    {
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      "target": "TwoDescent"
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    {
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    {
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      "target": "Seq"
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    {
      "kind": "statement_uses_definition",
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      "target": "SelmerWitness"
    },
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      "kind": "statement_uses_definition",
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      "target": "WeakMW"
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  ]
}