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        "kind": "planned_prerequisite",
        "source": "IR005",
        "target": "TR001"
      },
      {
        "kind": "planned_prerequisite",
        "source": "IR026",
        "target": "TR001"
      },
      {
        "kind": "proposed_definition_use",
        "source": "IRD25",
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      {
        "kind": "proposed_definition_use",
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      {
        "kind": "planned_prerequisite",
        "source": "IR029",
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      },
      {
        "kind": "planned_prerequisite",
        "source": "IR044",
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      },
      {
        "kind": "planned_prerequisite",
        "source": "TR001",
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        "kind": "proposed_definition_use",
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        "kind": "planned_prerequisite",
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        "kind": "planned_prerequisite",
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        "kind": "planned_prerequisite",
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        "kind": "planned_prerequisite",
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        "kind": "planned_prerequisite",
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      {
        "kind": "planned_prerequisite",
        "source": "IR054",
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      {
        "kind": "planned_prerequisite",
        "source": "IR060",
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      {
        "kind": "planned_prerequisite",
        "source": "IR064",
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      {
        "kind": "planned_prerequisite",
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        "kind": "planned_prerequisite",
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      {
        "kind": "planned_prerequisite",
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      {
        "kind": "planned_prerequisite",
        "source": "TR004",
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        "kind": "planned_prerequisite",
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      {
        "kind": "planned_prerequisite",
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        "kind": "proposed_definition_use",
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        "kind": "engineering_prerequisite",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG001",
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        "kind": "engineering_prerequisite",
        "source": "ENG002",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG001",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG002",
        "target": "ENG004"
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG003",
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      {
        "kind": "engineering_prerequisite",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG005",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG003",
        "target": "ENG007"
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      {
        "kind": "engineering_prerequisite",
        "source": "IR072",
        "target": "ENG008"
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      {
        "kind": "engineering_prerequisite",
        "source": "IR073",
        "target": "ENG008"
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      {
        "kind": "engineering_prerequisite",
        "source": "IR074",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG006",
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        "kind": "engineering_prerequisite",
        "source": "ENG007",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG001",
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      {
        "kind": "engineering_prerequisite",
        "source": "ENG003",
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    ],
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    },
    "semantics": "Planned dependencies, never verified proof edges"
  },
  "date": "2026-09-19",
  "execution_priority": [
    "irrationality",
    "transcendence"
  ],
  "grand_campaign": {
    "domain": "D06",
    "existing_goal_count": 120,
    "family": "F13",
    "goals": [
      "G121",
      "G122"
    ],
    "parent": "book/_static/constructive-jordan-campaign-v35"
  },
  "groups": {
    "A": "Arithmetic contracts and finite certificates",
    "B": "Explicit upper and lower bounds",
    "E": "Automation, reconstruction, and release gates",
    "H": "Finite confluent interpolation",
    "L": "Small integer kernels and auxiliary coefficients",
    "P": "Perturbation and positive irrationality",
    "Q": "Exact quadratic arithmetic",
    "S": "Certified square root, logarithm, and exponential",
    "T": "Transcendence: phase two, not current execution",
    "V": "Moment polynomials and bounded nonvanishing"
  },
  "methods": {
    "certificate-reconstruction": "New fail-closed adapter work, not presently implemented or trusted.",
    "native-induction": "Agent fixes the induction invariant once; deterministic generators build base/step proof obligations and native proof terms.",
    "native-numeral": "Exact integers/Fraction computation plus proof-producing normalization; floats are not evidence.",
    "native-order": "Native arithmetic reconstruction first; Z3 QF_LIA suggests coefficients, cases or substitutions. Nonlinear obligations must be decomposed or certified separately.",
    "native-ring": "Existing proof-producing ring/compact arithmetic; exact CAS only suggests identities.",
    "native-search": "Bounded HA logical search and checked-premise retrieval; E/Vampire may suggest instantiations after export/reconstruction gates.",
    "structural-check": "Deterministic schema, graph, provenance and mutation tests; not a mathematical proof."
  },
  "next_target": "TR006",
  "nodes": [
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "d>0; represented value is (p-m)/d. No coprimality or canonical-code equality is assumed.",
      "deps": [],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD01",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
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        "m",
        "d"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "RatRep"
    },
    {
      "arity": 6,
      "authority": "planning_only",
      "contract": "RatRep(p,m,d) and RatRep(P,M,D) and p*D+M*d=m*D+P*d.",
      "deps": [
        "IRD01"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD02",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
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        "m",
        "d",
        "P",
        "M",
        "D"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "RatEq"
    },
    {
      "arity": 6,
      "authority": "planning_only",
      "contract": "RatRep(p,m,d) and RatRep(P,M,D) and exists k. p*D+M*d+S(k)=m*D+P*d.",
      "deps": [
        "IRD01"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD03",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "p",
        "m",
        "d",
        "P",
        "M",
        "D"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "RatLt"
    },
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "Decode three rational triples; RatLt-or-RatEq(lo,q) and RatLt-or-RatEq(q,hi). Decoding witnesses remain explicit.",
      "deps": [
        "IRD02",
        "IRD03"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD04",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "q",
        "lo",
        "hi"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "RatInterval"
    },
    {
      "arity": 4,
      "authority": "planning_only",
      "contract": "A beta-coded finite addition/multiplication execution; all input/output triples have positive denominators. It does not assert any analytic estimate.",
      "deps": [
        "IRD01",
        "IRD02"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD05",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "xs",
        "length",
        "trace",
        "result"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "RatFold"
    },
    {
      "arity": 4,
      "authority": "planning_only",
      "contract": "pow=2^k by the existing Pow graph, and integer-square-root trace establishes z²<=2*pow²<(z+1)². Bracket endpoints z/pow and (z+1)/pow.",
      "deps": [
        "IRD04"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD06",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "k",
        "z",
        "pow",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "Sqrt2Bracket"
    },
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "value=2*sum(j<K,1/((2*j+1)*3^(2*j+1))) by a rational fold trace; no limit or inverse-exponential assertion is part of the definition.",
      "deps": [
        "IRD05"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD07",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "K",
        "value",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "Log2Partial"
    },
    {
      "arity": 4,
      "authority": "planning_only",
      "contract": "value=sum(j<=N,x^j/j!) by witnessed powers, factorials and a rational fold; denominator positivity is explicit.",
      "deps": [
        "IRD05"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD08",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
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        "N",
        "value",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "ExpPartial"
    },
    {
      "arity": 5,
      "authority": "planning_only",
      "contract": "k=n+8; s=floor_sqrt(2*2^(2*k))/2^k; L=Log2Partial(k); t=L/s; u=ExpPartial(t,k+2). trace witnesses these actual computations; (up-um)/ud=u. No error bound is assumed.",
      "deps": [
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        "IRD07",
        "IRD08",
        "IRD02"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD09",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
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        "up",
        "um",
        "ud",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "CApprox"
    },
    {
      "arity": 9,
      "authority": "planning_only",
      "contract": "b>0 and CApprox(n,up,um,ud,trace) and e=2^n and [(b*um+ap*ud)*e+2*b*ud < (b*up+am*ud)*e or (b*up+am*ud)*e+2*b*ud < (b*um+ap*ud)*e].",
      "deps": [
        "IRD09"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD10",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
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        "am",
        "b",
        "n",
        "up",
        "um",
        "ud",
        "e",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "IrrCert"
    },
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "A,B are witnessed signed integers and D>0; denotes (A+B*sqrt2)/D. sqrt2 is semantic shorthand only, not a kernel term.",
      "deps": [
        "IRD01"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD11",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "A",
        "B",
        "D"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "QuadRep"
    },
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "Decode quadratic triples; z represents ((A*C+2*B*E)+(A*E+B*C)*sqrt2)/(D*F). Equality is of coefficients after cross multiplication.",
      "deps": [
        "IRD11",
        "IRD02"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD12",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "x",
        "y",
        "z"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "QuadMul"
    },
    {
      "arity": 2,
      "authority": "planning_only",
      "contract": "For x=(A+B*sqrt2)/D, norm is the signed rational (A²-2*B²)/D².",
      "deps": [
        "IRD11",
        "IRD01"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD13",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "x",
        "norm"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "QuadNorm"
    },
    {
      "arity": 7,
      "authority": "planning_only",
      "contract": "H=max(2,abs(ap-am),b), b>0, q>0, 28 divides q, N=q²=28*n. A reviewed choice of q(H) is a theorem, not a premise silently hidden here.",
      "deps": [],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD14",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "ap",
        "am",
        "b",
        "H",
        "q",
        "n",
        "N"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "AuxParameters"
    },
    {
      "arity": 4,
      "authority": "planning_only",
      "contract": "i<q and j<q and lambda is the quadratic pair (i,j,1).",
      "deps": [
        "IRD11"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD15",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "q",
        "i",
        "j",
        "lambda"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "Frequency"
    },
    {
      "arity": 8,
      "authority": "planning_only",
      "contract": "value=sum(i,j<q, coeff[i,j]*(i+j*sqrt2)^k*(sqrt2)^(i*ell)*(a/b)^(j*ell)) in exact quadratic arithmetic. Signed coefficients and 0^0=1 are explicit.",
      "deps": [
        "IRD12",
        "IRD15",
        "IRD05"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD16",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "a",
        "b",
        "q",
        "coeff",
        "ell",
        "k",
        "value",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "AuxJet"
    },
    {
      "arity": 6,
      "authority": "planning_only",
      "contract": "Two signed integer coordinate rows per (ell<7,k<n), obtained from AuxJet by the uniform multiplier b^(6*(q-1)); columns enumerate i*q+j.",
      "deps": [
        "IRD16",
        "IRD14"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD17",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "a",
        "b",
        "q",
        "n",
        "matrix",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "AuxMatrix"
    },
    {
      "arity": 5,
      "authority": "planning_only",
      "contract": "coeff is an actual length-N signed integer vector, not all zero, max abs(coeff)<=B, and every decoded matrix-row dot product is zero.",
      "deps": [
        "IRD17"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD18",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "matrix",
        "N",
        "coeff",
        "B",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "AuxKernelVector"
    },
    {
      "arity": 5,
      "authority": "planning_only",
      "contract": "Rational enclosures for x_ell=ell*Log2/2, obtained from the fixed Log2Partial sequence, for ell<7.",
      "deps": [
        "IRD07",
        "IRD04"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD19",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "ell",
        "precision",
        "lo",
        "hi",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "NodeBracket"
    },
    {
      "arity": 4,
      "authority": "planning_only",
      "contract": "Finite sum of all monomials of total degree in the listed nodes, with explicit weak-composition enumeration.",
      "deps": [
        "IRD05"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD20",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "nodes",
        "degree",
        "value",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "HomogeneousSum"
    },
    {
      "arity": 5,
      "authority": "planning_only",
      "contract": "Finite repeated-node divided difference of a polynomial, defined algebraically by a recurrence/monomial table. Equality cases use multiplicities, not division by zero.",
      "deps": [
        "IRD20"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD21",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "nodes",
        "mults",
        "polynomial",
        "value",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "ConfluentFunctional"
    },
    {
      "arity": 6,
      "authority": "planning_only",
      "contract": "Explicit finite product and truncated reciprocal-series construction of a cardinal Hermite polynomial. Its cardinality identities are separate theorems.",
      "deps": [
        "IRD05",
        "IRD21"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD22",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "nodes",
        "mults",
        "ell",
        "k",
        "polynomial",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "HermiteBasis"
    },
    {
      "arity": 9,
      "authority": "planning_only",
      "contract": "Finite positive rational expression bounding the difference between AuxJet at a/b and the fixed-exponential jet, under |c-a/b|<=eps. This definition records the expression, not its validity.",
      "deps": [
        "IRD16",
        "IRD08"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD23",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "a",
        "b",
        "q",
        "coeff",
        "ell",
        "k",
        "eps",
        "bound",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "JetErrorBound"
    },
    {
      "arity": 9,
      "authority": "planning_only",
      "contract": "A finite computation selecting positive rational error budgets and dyadic precision from explicit bounds; no irrationality or search-termination hypothesis is allowed.",
      "deps": [
        "IRD14",
        "IRD23"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD24",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "H",
        "q",
        "n",
        "B",
        "K",
        "W",
        "eps",
        "precision",
        "trace"
      ],
      "phase": 1,
      "status": "proposed",
      "title": "SeparationSchedule"
    },
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "Decode an actual signed coefficient list; nonzero means some decoded coefficient is nonzero. Reuse the existing polynomial representation after argument-alignment review.",
      "deps": [],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD25",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "code",
        "degree",
        "trace"
      ],
      "phase": 2,
      "status": "proposed",
      "title": "IntegerPolynomial"
    },
    {
      "arity": 3,
      "authority": "planning_only",
      "contract": "A CApprox computation and exact rational evaluation establish |P(u_precision)|>2*M_P*2^(-precision), with M_P=1+sum(j>=1,j*abs(a_j)*2^(j-1)).",
      "deps": [
        "IRD09",
        "IRD25"
      ],
      "expansion_ast_sha256": null,
      "group": "definitions",
      "id": "IRD26",
      "kernel_definition_id": null,
      "kind": "definition",
      "parameters": [
        "poly",
        "precision",
        "witness"
      ],
      "phase": 2,
      "status": "proposed",
      "title": "TransCert"
    },
    {
      "authority": "planning_only",
      "contract": "Positive-denominator RatEq is reflexive, symmetric and transitive; signed numerator pairs may be noncanonical.",
      "definitions": [
        "IRD01",
        "IRD02"
      ],
      "deps": [],
      "group": "A",
      "id": "IR001",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Rational representation equivalence",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Cross-multiplied addition, product and negation preserve RatEq; every constructed denominator is positive.",
      "definitions": [
        "IRD02"
      ],
      "deps": [
        "IR001"
      ],
      "group": "A",
      "id": "IR002",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Rational operations respect representation",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "RatLt and RatEq are decidable; exactly one of x<y,x=y,y<x holds for valid triples; positive-denominator clearing preserves strict inequalities.",
      "definitions": [
        "IRD03"
      ],
      "deps": [
        "IR001"
      ],
      "group": "A",
      "id": "IR003",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Rational order and decision",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Triangle/product inequalities and inclusion-preserving addition, multiplication and reciprocal on intervals with positive lower endpoint.",
      "definitions": [
        "IRD04"
      ],
      "deps": [
        "IR002",
        "IR003"
      ],
      "group": "A",
      "id": "IR004",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Absolute value and interval arithmetic",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Every coded finite rational list has addition/product/factorial/power fold witnesses; results are unique up to RatEq, not unique codes.",
      "definitions": [
        "IRD05"
      ],
      "deps": [
        "IR002"
      ],
      "group": "A",
      "id": "IR005",
      "independent_lean_receipt": null,
      "induction": "list length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite rational folds",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For each positive rational eta and natural A, construct t with (A+1)*2^(-t)<eta by an explicit natural bound; prove power monotonicity.",
      "definitions": [],
      "deps": [
        "IR003",
        "IR005"
      ],
      "group": "A",
      "id": "IR006",
      "independent_lean_receipt": null,
      "induction": "natural exponent",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Dyadic domination",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "An explicit map from a finite box with cardinality strictly exceeding a finite target box has two distinct inputs with the same output.",
      "definitions": [],
      "deps": [
        "IR005"
      ],
      "group": "A",
      "id": "IR007",
      "independent_lean_receipt": null,
      "induction": "finite target cardinality",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "reuse-audit",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite pigeonhole",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For decidable D and a witness i<N with D(i), construct least r<N with D(r) and all k<r satisfying not D(k).",
      "definitions": [],
      "deps": [
        "IR003"
      ],
      "group": "A",
      "id": "IR008",
      "independent_lean_receipt": null,
      "induction": "N",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Bounded decidable minimum",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For integer e>=1, x^e-y^e=(x-y)*sum(j<e,x^(e-1-j)*y^j); if |x|,|y|<=H, then |x^e-y^e|<=e*H^(e-1)*|x-y|. Treat e=0 separately.",
      "definitions": [],
      "deps": [
        "IR004",
        "IR005"
      ],
      "group": "A",
      "id": "IR009",
      "independent_lean_receipt": null,
      "induction": "e",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Power difference factorization",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For 0<=rho<1, every finite tail sum from K to K+M is <=rho^K/(1-rho), with denominator and rho=0 boundaries explicit.",
      "definitions": [],
      "deps": [
        "IR004",
        "IR005"
      ],
      "group": "A",
      "id": "IR010",
      "independent_lean_receipt": null,
      "induction": "M",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Geometric tail arithmetic",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For t>=1, (t+1)!>=2^t; for r>=1,m>=1, (mr)!>=r! * r^((m-1)r). All quotient formulations are derived by positive clearing.",
      "definitions": [],
      "deps": [
        "IR003",
        "IR005"
      ],
      "group": "A",
      "id": "IR011",
      "independent_lean_receipt": null,
      "induction": "t and factorial-product length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Factorial lower bounds",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For the finitely many named rational-sequence codes used here, prove addition/product/reciprocal enclosure transport with explicit input-precision moduli; no quantification over arbitrary functions.",
      "definitions": [
        "IRD04"
      ],
      "deps": [
        "IR004",
        "IR006"
      ],
      "group": "A",
      "id": "IR012",
      "independent_lean_receipt": null,
      "induction": "precision",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Approximation operations without real sorts",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For every v, construct z with z²<=v<(z+1)² by a bounded binary-search or existing division trace; establish uniqueness of z.",
      "definitions": [
        "IRD06"
      ],
      "deps": [
        "IR003",
        "IR008"
      ],
      "group": "S",
      "id": "IR013",
      "independent_lean_receipt": null,
      "induction": "search interval length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "reuse-audit",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Integer square root totality",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For k>=1 and z²<=2*2^(2k)<(z+1)², 1<=z/2^k and the interval [z/2^k,(z+1)/2^k] has width 2^-k; enclosures are compatible across precisions.",
      "definitions": [
        "IRD06"
      ],
      "deps": [
        "IR013",
        "IR011",
        "IR012"
      ],
      "group": "S",
      "id": "IR014",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Dyadic sqrt2 enclosures",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "The fixed bracket sequence squares to 2 with an explicit multiplication modulus and lies strictly between 1 and 3/2. Derive the exact reciprocal and conjugation identities.",
      "definitions": [
        "IRD06"
      ],
      "deps": [
        "IR014",
        "IR012"
      ],
      "group": "S",
      "id": "IR015",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Sqrt2 algebra and strict bounds",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For natural A,B, A²=2*B² implies A=B=0; signed versions follow by absolute values. Replay in HA, not merely the separate Lean demo.",
      "definitions": [],
      "deps": [
        "IR003",
        "IR008"
      ],
      "group": "S",
      "id": "IR016",
      "independent_lean_receipt": null,
      "induction": "strong induction on A+B",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "reuse-audit",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Even-square descent",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For L_K=2*sum(j<K,1/((2j+1)*3^(2j+1))), every finite extension increment lies in [0,9^-K]; construct a fixed compatible sequence from these bounds.",
      "definitions": [
        "IRD07"
      ],
      "deps": [
        "IR005",
        "IR010",
        "IR012"
      ],
      "group": "S",
      "id": "IR017",
      "independent_lean_receipt": null,
      "induction": "finite extension length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Logarithm series remainder",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "2/3<=L<1 for the fixed log series; x_ell=ell*L/2 satisfies 0<=x_ell<3 and x_(ell+1)-x_ell>=1/3 for ell<6. A weaker [0,7] enclosure is allowed in bounds.",
      "definitions": [
        "IRD19"
      ],
      "deps": [
        "IR017",
        "IR012"
      ],
      "group": "S",
      "id": "IR018",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Logarithm interval and node gaps",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For every rational x and N, construct ExpPartial(x,N) with witnessed factorial and power tables; prove the successor recurrence and representation independence.",
      "definitions": [
        "IRD08"
      ],
      "deps": [
        "IR005"
      ],
      "group": "S",
      "id": "IR019",
      "independent_lean_receipt": null,
      "induction": "N",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Exponential partial-sum totality",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For x>=0 and N+2>=2*x, bound each finite tail beyond N by 2*x^(N+1)/(N+1)!; give an explicit N(x,t) making this <2^-t. Handle x=0 separately.",
      "definitions": [
        "IRD08"
      ],
      "deps": [
        "IR019",
        "IR010",
        "IR011",
        "IR006"
      ],
      "group": "S",
      "id": "IR020",
      "independent_lean_receipt": null,
      "induction": "tail length and precision schedule",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Exponential explicit tail",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "The degree<=N coefficients of ExpPartial(x+z,N) equal the corresponding convolution coefficients of ExpPartial(x,N)*ExpPartial(z,N); bound the discarded terms explicitly.",
      "definitions": [
        "IRD08"
      ],
      "deps": [
        "IR009",
        "IR019",
        "IR020"
      ],
      "group": "S",
      "id": "IR021",
      "independent_lean_receipt": null,
      "induction": "N",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite binomial convolution",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For fixed rational-sequence arguments with supplied enclosures, exp(x+z)=exp(x)*exp(z), exp(0)=1, and exp(j*x)=exp(x)^j, witnessed to every finite accuracy.",
      "definitions": [
        "IRD08"
      ],
      "deps": [
        "IR012",
        "IR020",
        "IR021"
      ],
      "group": "S",
      "id": "IR022",
      "independent_lean_receipt": null,
      "induction": "j and precision",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Exponential addition and integer powers",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "On [0,M], positive-series estimates give positivity/monotonicity and |exp(x)-exp(y)|<=3^(ceil(M)+1)*|x-y|; on [0,1] improve the bound to 3. Prove e<3 by a factorial tail.",
      "definitions": [
        "IRD08"
      ],
      "deps": [
        "IR020",
        "IR022",
        "IR010"
      ],
      "group": "S",
      "id": "IR023",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Exponential order and Lipschitz",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For L given by IR017, specialize IR079-81 at z=1/3 to obtain exp(L)=2. Do not assume this identity in Log2Partial or appeal to an imported real logarithm.",
      "definitions": [
        "IRD07",
        "IRD08"
      ],
      "deps": [
        "IR017",
        "IR020",
        "IR021",
        "IR022",
        "IR079",
        "IR080",
        "IR081"
      ],
      "group": "S",
      "id": "IR024",
      "independent_lean_receipt": null,
      "induction": "finite coefficient identities and explicit precision",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Log-exp inverse at two",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For every n, CApprox(n,up,um,ud,trace) has witnesses with ud>0; results are unique up to RatEq. No unbounded numerical search is part of this algorithm.",
      "definitions": [
        "IRD09"
      ],
      "deps": [
        "IR014",
        "IR017",
        "IR019",
        "IR005"
      ],
      "group": "S",
      "id": "IR025",
      "independent_lean_receipt": null,
      "induction": "finite algorithm traces",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Canonical approximation totality",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For k=n+8, the sqrt/log quotient error is <=2*2^-k and exponential truncation error <=2^-k; hence |u_n-exp(L/sqrt2)|<=7*2^-k<2^-n and 1<=u_n<=2.",
      "definitions": [
        "IRD09"
      ],
      "deps": [
        "IR015",
        "IR020",
        "IR023",
        "IR024",
        "IR025"
      ],
      "group": "S",
      "id": "IR026",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Canonical approximation accuracy",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "From exp(L)=2 and positivity, exp(L/2)=sqrt2 and exp(L/sqrt2)=exp(sqrt2*L/2). Thus the fixed approximation sequence denotes the positive real power (sqrt2)^(sqrt2).",
      "definitions": [
        "IRD09"
      ],
      "deps": [
        "IR015",
        "IR022",
        "IR024",
        "IR026"
      ],
      "group": "S",
      "id": "IR027",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Identification with the requested constant",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Establish 3/2<c<7/4 from one exact rational CApprox computation and IR026; emit a native certificate for the finite rational inequalities.",
      "definitions": [
        "IRD09"
      ],
      "deps": [
        "IR026"
      ],
      "group": "S",
      "id": "IR028",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-numeral",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "A strict coarse enclosure",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "QuadRep addition/multiplication/conjugation respect cross-multiplied coefficient equivalence and satisfy commutative-ring laws.",
      "definitions": [
        "IRD11",
        "IRD12"
      ],
      "deps": [
        "IR002",
        "IR005"
      ],
      "group": "Q",
      "id": "IR029",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Quadratic ring operations",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "(A+B*sqrt2)/D=0 iff A=B=0; equality of two triples is equivalent to two signed integer equalities after clearing denominators.",
      "definitions": [
        "IRD11"
      ],
      "deps": [
        "IR016",
        "IR029",
        "IR015"
      ],
      "group": "Q",
      "id": "IR030",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Quadratic equality is decidable",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "N(x)=x*conj(x)=(A²-2B²)/D² and N(x*y)=N(x)*N(y).",
      "definitions": [
        "IRD13"
      ],
      "deps": [
        "IR029"
      ],
      "group": "Q",
      "id": "IR031",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Norm identity and multiplicativity",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "If A,B are integers not both zero, abs(A²-2B²)>=1; hence |A+B*sqrt2|>=1/(|A|+2*|B|). Denominator is positive.",
      "definitions": [
        "IRD13"
      ],
      "deps": [
        "IR016",
        "IR030",
        "IR031",
        "IR015",
        "IR004"
      ],
      "group": "Q",
      "id": "IR032",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Integral quadratic norm separation",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For integer pair (A,B), powers have integer-pair traces; weighted height h(A,B)=|A|+2|B| is submultiplicative and h(i,j)<=3q for i,j<q.",
      "definitions": [
        "IRD12",
        "IRD15"
      ],
      "deps": [
        "IR029",
        "IR005",
        "IR004"
      ],
      "group": "Q",
      "id": "IR033",
      "independent_lean_receipt": null,
      "induction": "power exponent",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Quadratic powers and coefficient height",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For distinct (i,j),(I,J) in [0,q)^2, their frequencies differ; give a nonzero quadratic norm and rational lower bound >=1/(3q) on the absolute gap.",
      "definitions": [
        "IRD15"
      ],
      "deps": [
        "IR032",
        "IR033"
      ],
      "group": "Q",
      "id": "IR034",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Distinct frequencies with quantitative gap",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "If D>0 and D*g=A+B*sqrt2!=0, then |g|>=1/(D*(|A|+2|B|)); do not conflate the denominator D with a square or omit it.",
      "definitions": [
        "IRD11",
        "IRD13"
      ],
      "deps": [
        "IR032",
        "IR004"
      ],
      "group": "Q",
      "id": "IR035",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Cleared rational quadratic lower bound",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "q is a positive multiple of 28, N=q², n=N/28: n>=q, 14*n=N/2 and N=28*n. Dimensions are exact integers.",
      "definitions": [
        "IRD14"
      ],
      "deps": [
        "IR003",
        "IR005"
      ],
      "group": "L",
      "id": "IR036",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Auxiliary parameter arithmetic",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Column (i,j) maps bijectively to i*q+j<N; rows (ell,k,coordinate) biject with 14*n positions. Construct all tables from beta traces.",
      "definitions": [
        "IRD17"
      ],
      "deps": [
        "IR036",
        "IR005"
      ],
      "group": "L",
      "id": "IR037",
      "independent_lean_receipt": null,
      "induction": "table length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Matrix row/column enumerations",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "D=b^(6*(q-1)) clears every AuxJet coefficient for ell<7,k<n; powers of sqrt2 introduce no denominators. Equivalence of cleared coordinate zero and quadratic zero is proved.",
      "definitions": [
        "IRD16",
        "IRD17"
      ],
      "deps": [
        "IR033",
        "IR030",
        "IR037"
      ],
      "group": "L",
      "id": "IR038",
      "independent_lean_receipt": null,
      "induction": "finite row/column enumeration",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Uniform denominator clearing",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For H=max(2,|a|,b), each cleared integer matrix entry has absolute value <=A=(3q)^n*(2H)^(6q). Prove inequalities symbolically; never materialize this huge matrix for the universal proof.",
      "definitions": [
        "IRD17"
      ],
      "deps": [
        "IR038",
        "IR033",
        "IR009"
      ],
      "group": "L",
      "id": "IR039",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Auxiliary matrix height",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For an M by N integer matrix bounded by A>=1 and x in {0,...,2NA}^N, each image coordinate lies in [-2N²A²,2N²A²].",
      "definitions": [
        "IRD18"
      ],
      "deps": [
        "IR005",
        "IR004"
      ],
      "group": "L",
      "id": "IR040",
      "independent_lean_receipt": null,
      "induction": "dot-product length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Linear-map image box",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "If N=2M>0 and A>=1, (2NA+1)^N>(4N²A²+1)^M. Prove the base inequality by ring normalization and lift through positive powers.",
      "definitions": [],
      "deps": [
        "IR011",
        "IR003"
      ],
      "group": "L",
      "id": "IR041",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Strict box cardinality inequality",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Combine IR007,IR040,IR041: construct nonzero signed beta with matrix*beta=0 and max|beta|<=2NA; handle zero matrix separately if A=0 is exposed by an API.",
      "definitions": [
        "IRD18"
      ],
      "deps": [
        "IR007",
        "IR040",
        "IR041"
      ],
      "group": "L",
      "id": "IR042",
      "independent_lean_receipt": null,
      "induction": "finite-map construction",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Small nonzero integer kernel vector",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For B=2*N*(3q)^n*(2H)^(6q), construct beta not all zero, |beta|<=B, and AuxJet(a,b,q,beta,ell,k)=0 for every ell<7,k<n.",
      "definitions": [
        "IRD16",
        "IRD18"
      ],
      "deps": [
        "IR036",
        "IR039",
        "IR042",
        "IR038"
      ],
      "group": "L",
      "id": "IR043",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-search",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Auxiliary low jets vanish algebraically",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For each t<N construct P_t(X)=product(u<N,u!=t,X-lambda_u), its coefficient list of degree<N, and prove evaluation at every frequency. No determinant library is required.",
      "definitions": [
        "IRD15"
      ],
      "deps": [
        "IR029",
        "IR005",
        "IR009"
      ],
      "group": "V",
      "id": "IR044",
      "independent_lean_receipt": null,
      "induction": "finite factor-list length",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Annihilating polynomial construction",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Writing P_t=sum(k<N,p_tk*X^k), prove sum(k<N,p_tk*A_(0,k))=beta_t*product(u!=t,lambda_t-lambda_u) by finite sum interchange and polynomial evaluation.",
      "definitions": [
        "IRD15",
        "IRD16"
      ],
      "deps": [
        "IR044",
        "IR005",
        "IR029"
      ],
      "group": "V",
      "id": "IR045",
      "independent_lean_receipt": null,
      "induction": "finite double sums",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Moment polynomial identity",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "A finite product of nonzero quadratic elements is nonzero, by norm multiplicativity and integer no-zero-divisors.",
      "definitions": [
        "IRD13"
      ],
      "deps": [
        "IR030",
        "IR031",
        "IR005"
      ],
      "group": "V",
      "id": "IR046",
      "independent_lean_receipt": null,
      "induction": "factor count",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Nonzero quadratic products",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For nonzero beta and distinct frequencies, some k<N satisfies sum beta_j*lambda_j^k !=0. Use IR045 at a nonzero coefficient and bounded decidable search; no determinant or infinite-series argument.",
      "definitions": [
        "IRD16"
      ],
      "deps": [
        "IR034",
        "IR045",
        "IR046",
        "IR043",
        "IR008"
      ],
      "group": "V",
      "id": "IR047",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-search",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Bounded nonzero jet at zero",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Decidable bounded search yields n<=r<N and ell0<7 with A_(ell0,r)!=0, while A_(ell,k)=0 for all ell<7,k<r. Minimality is across all seven nodes, not just zero.",
      "definitions": [
        "IRD16"
      ],
      "deps": [
        "IR008",
        "IR030",
        "IR043",
        "IR047"
      ],
      "group": "V",
      "id": "IR048",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-search",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Least nonzero jet across all nodes",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For selected r, bound the cleared jet and its conjugate; prove |A_(ell0,r)|>=1/K with K=N*B*(3q)^r*(2H²)^(6q). Audit all b-denominator factors explicitly.",
      "definitions": [
        "IRD16",
        "IRD13"
      ],
      "deps": [
        "IR035",
        "IR033",
        "IR038",
        "IR048",
        "IR039"
      ],
      "group": "V",
      "id": "IR049",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Selected jet height and separation",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Construct the weak compositions of s into N+1 parts; count them as binomial(N+s,s), and implement the complete homogeneous sum h_s.",
      "definitions": [
        "IRD20"
      ],
      "deps": [
        "IR005",
        "IR007"
      ],
      "group": "H",
      "id": "IR050",
      "independent_lean_receipt": null,
      "induction": "N+s",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Weak compositions and homogeneous sums",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "The algebraic repeated-node functional of order N sends X^j to 0 if j<N, and X^(N+s) to h_s(t_0,...,t_N), without assuming distinct nodes.",
      "definitions": [
        "IRD21"
      ],
      "deps": [
        "IR050",
        "IR009"
      ],
      "group": "H",
      "id": "IR051",
      "independent_lean_receipt": null,
      "induction": "N and monomial degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Monomial divided differences",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For 0<=t_i<=M, 0<=h_s<=binomial(N+s,s)*M^s. This includes s=0, M=0 and repeated nodes.",
      "definitions": [
        "IRD20"
      ],
      "deps": [
        "IR050",
        "IR004"
      ],
      "group": "H",
      "id": "IR052",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Homogeneous-sum enclosure",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "binomial(N+s,s)/(N+s)!=1/(N!*s!); derive by positive integer factorial identities.",
      "definitions": [],
      "deps": [
        "IR011",
        "IR005"
      ],
      "group": "H",
      "id": "IR053",
      "independent_lean_receipt": null,
      "induction": "s",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Factorial-binomial cancellation",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Apply IR051-53 to ExpPartial(lambda*t,J): for nodes in [0,M] and lambda>=0, its order-N functional is bounded by lambda^N/N!*ExpPartial(lambda*M,max(J-N,0)), with J<N handled separately.",
      "definitions": [
        "IRD08",
        "IRD21"
      ],
      "deps": [
        "IR019",
        "IR051",
        "IR052",
        "IR053"
      ],
      "group": "H",
      "id": "IR054",
      "independent_lean_receipt": null,
      "induction": "finite polynomial degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite exponential divided-difference estimate",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Construct H_(ell,k) for multiplicities s_ell>0 and distinct nodes such that H_(ell,k)^(j)(x_i)=delta_(i,ell)*delta_(j,k) for j<s_i. Include the k! normalization explicitly.",
      "definitions": [
        "IRD22"
      ],
      "deps": [
        "IR009",
        "IR005",
        "IR018"
      ],
      "group": "H",
      "id": "IR055",
      "independent_lean_receipt": null,
      "induction": "truncated reciprocal-series degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Polynomial Hermite cardinal basis",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For any rational polynomial f, repeated-node divided differences equal the corresponding finite linear combination of its node derivatives. Specialize multiplicities r+1 at ell0, r elsewhere, total order 7r.",
      "definitions": [
        "IRD21",
        "IRD22"
      ],
      "deps": [
        "IR051",
        "IR055"
      ],
      "group": "H",
      "id": "IR056",
      "independent_lean_receipt": null,
      "induction": "polynomial degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite confluent interpolation identity",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For L0=L/2 in [1/4,1/2], M=7r and multiplicities r+1 at ell0,r elsewhere: C_jk=[w^(m_j-1-k)] product(h!=j,(x_j-x_h+w)^(-m_h)); |C_jk|<=2^(21r), |P|<=12^r, P=product(h!=ell0,(x_ell0-x_h)^r). The lower-jet aggregate is bounded by W=7r*r!*12^r*2^(21r).",
      "definitions": [
        "IRD22"
      ],
      "deps": [
        "IR055",
        "IR056",
        "IR018",
        "IR004"
      ],
      "group": "H",
      "id": "IR057",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Explicit interpolation coefficient bound",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For the finitely many derivatives and functional coefficients in IR056, construct J(t,N,lambda,W) making every omitted Taylor contribution <2^-t, including the multiplied functional error. Explicitly bound all nodes and frequencies.",
      "definitions": [
        "IRD08",
        "IRD21"
      ],
      "deps": [
        "IR020",
        "IR054",
        "IR057",
        "IR012",
        "IR077",
        "IR078"
      ],
      "group": "H",
      "id": "IR058",
      "independent_lean_receipt": null,
      "induction": "tail precision schedule",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Polynomial-to-exponential tail transfer",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "If all true exponential jets below r vanish at every node, then |F^(r)(x_ell0)| <= r!*12^r/(7r)! * N*B*(3q)^(7r)*2^(15q). Nodes lie in [0,3], so exp(9q)<3^(9q)<2^(15q). Derive via IR056/58, not Rolle or compactness.",
      "definitions": [
        "IRD16",
        "IRD21"
      ],
      "deps": [
        "IR054",
        "IR056",
        "IR057",
        "IR058",
        "IR022",
        "IR023"
      ],
      "group": "H",
      "id": "IR059",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Zero-jet interpolation estimate",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Without assuming c=a/b: bound the selected actual jet by the IR059 analytic term plus W times the maximum of the true lower-jet residuals. Include normalization at the selected node and all 7r lower jets.",
      "definitions": [
        "IRD21",
        "IRD22",
        "IRD23"
      ],
      "deps": [
        "IR056",
        "IR057",
        "IR058"
      ],
      "group": "H",
      "id": "IR060",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Approximate-zero interpolation estimate",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For x_ell=ell*L/2, exp((i+j*sqrt2)*x_ell)=(sqrt2)^(i*ell)*c^(j*ell); jets multiply by (i+j*sqrt2)^k. Prove this through finite exponential identities and tails.",
      "definitions": [
        "IRD16",
        "IRD19"
      ],
      "deps": [
        "IR027",
        "IR022",
        "IR033",
        "IR058"
      ],
      "group": "B",
      "id": "IR061",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Exponential jet identity",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For 0<=t<=3, frequencies<=3q and |beta|<=B, bound the derivative-order-7r series by N*B*(3q)^(7r)*2^(15q), using e<3 and 3^9<2^15.",
      "definitions": [
        "IRD16",
        "IRD08"
      ],
      "deps": [
        "IR023",
        "IR033",
        "IR043",
        "IR058"
      ],
      "group": "B",
      "id": "IR062",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Growth on the interpolation interval",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "With n<=r and q²=28n, prove r!/(7r)!<=r^(-6r) and q^(8r)<=28^(4r)*r^(4r), by cleared positive inequalities.",
      "definitions": [],
      "deps": [
        "IR011",
        "IR036",
        "IR048"
      ],
      "group": "B",
      "id": "IR063",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Factorial and q-to-r descent",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Set q=28*2^44*H^12, n=q²/28. With U=N*B*12^r*(3q)^(7r)*2^(15q)*r!/(7r)!, prove K*U<=(2^88*H^24/r)^r<=28^(-r)<=1/4 for n<=r<q². Intermediate contracts: 4q^8<=2^(10r), q^(10r)<=(28r)^(5r), 2^55*3^11*7^5<=2^88. Never expand the auxiliary matrix at this bound.",
      "definitions": [
        "IRD14"
      ],
      "deps": [
        "IR049",
        "IR059",
        "IR062",
        "IR063"
      ],
      "group": "B",
      "id": "IR064",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Explicit combined gap",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "If the fixed c sequence equals a/b at every accuracy, IR061 identifies its jets with AuxJet; IR048/49/59/64 contradict one another. Conclude not(c=a/b) for b>0, without a Markov axiom.",
      "definitions": [
        "IRD16",
        "IRD09"
      ],
      "deps": [
        "IR048",
        "IR049",
        "IR059",
        "IR061",
        "IR064",
        "IR026"
      ],
      "group": "B",
      "id": "IR065",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-search",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Negative irrationality checkpoint",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For z=a/b outside [1,2], IR028 gives a positive explicit separation from c. Construct a precision certificate using IR006 and IR026; signed/negative/zero a are included.",
      "definitions": [
        "IRD10"
      ],
      "deps": [
        "IR028",
        "IR026",
        "IR006",
        "IR003"
      ],
      "group": "P",
      "id": "IR066",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Rational competitors outside the unit interval",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For z=a/b, H=max(2,|a|,b), c<=4, prove |F^(k)(x_ell)-A_(ell,k)(z)|<=J*|c-z| for ell<7,k<=r, J=6q*N*B*(3q)^r*(4H)^(6q). Use power telescoping, including exponent zero.",
      "definitions": [
        "IRD23"
      ],
      "deps": [
        "IR009",
        "IR061",
        "IR043",
        "IR048",
        "IR026"
      ],
      "group": "P",
      "id": "IR067",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Uniform perturbation of algebraic jets",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "With S=1+7r*r!*12^r*2^(21r), derive 1/K<=U+S*J*|c-z| in rational-sequence form. Compile the finite polynomial substitution errors and Taylor errors to total <=1/(4K); include selected-jet error and all 7r unselected jets.",
      "definitions": [
        "IRD23",
        "IRD24"
      ],
      "deps": [
        "IR048",
        "IR060",
        "IR067",
        "IR058",
        "IR049",
        "IR012",
        "IR075",
        "IR076",
        "IR078"
      ],
      "group": "P",
      "id": "IR068",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite accuracy removes vanishing assumptions",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Set epsilon=1/(4*K*S*J), all factors positive. A hypothetical |c-z|<=epsilon yields upper bound<=1/(2K), plus at most1/(4K) finite-evaluation error, contradicting the lower bound1/K. Establish the required rational implications, not a general real-order decision principle.",
      "definitions": [
        "IRD24"
      ],
      "deps": [
        "IR064",
        "IR068",
        "IR049",
        "IR003",
        "IR006"
      ],
      "group": "P",
      "id": "IR069",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Excluded neighborhood with rational slack",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Construct t with 2^t>=12*K*S*J. Failure of the decidable test |b*u_t-a|>2*b*2^-t implies |c-z|<=3*2^-t<=epsilon, contradicting IR069. Decidability of this single finite rational test yields the certificate in HA; no Markov rule is used.",
      "definitions": [
        "IRD10",
        "IRD24"
      ],
      "deps": [
        "IR069",
        "IR026",
        "IR006",
        "IR004",
        "IR003"
      ],
      "group": "P",
      "id": "IR070",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Decidable precision-to-certificate bridge",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "IrrCert implies |b*c-a|>b*2^-n>0 using IR026. This is a semantic explanation backed by rational-sequence inequalities, not a kernel real-number predicate.",
      "definitions": [
        "IRD10"
      ],
      "deps": [
        "IR026",
        "IR004"
      ],
      "group": "P",
      "id": "IR071",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-order",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Irrationality certificate soundness",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "forall ap am b. b>0 -> exists n up um ud e trace. IrrCert(ap,am,b,n,up,um,ud,e,trace). Split rational competitors inside/outside [1,2]; no classical rule, oracle, missing premise or degree/height restriction.",
      "definitions": [
        "IRD10"
      ],
      "deps": [
        "IR066",
        "IR070",
        "IR071",
        "IR025"
      ],
      "group": "P",
      "id": "IR072",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-search",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Full positive HA irrationality",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For every signed a and b>0, sequential exact evaluation of CApprox followed by the decidable certificate test halts. Termination follows from IR072; practical complexity is a separate question.",
      "definitions": [
        "IRD10"
      ],
      "deps": [
        "IR072",
        "IR003",
        "IR025"
      ],
      "group": "P",
      "id": "IR073",
      "independent_lean_receipt": null,
      "induction": "bounded search up to the witnessed precision",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Certificate-search totality",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Equivalent signed numerator pairs and rational representations yield the same irrationality conclusion; positive rescaling of a,b is supported without identifying raw trace codes.",
      "definitions": [
        "IRD10"
      ],
      "deps": [
        "IR072",
        "IR001",
        "IR002"
      ],
      "group": "P",
      "id": "IR074",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Representation-invariant endpoint",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For every finite signed/rational polynomial P, construct U,V,Q with P(X)=U+V*X+(X²-2)*Q(X). Emit an identity certificate; substitution at approximate sqrt2 has an explicit residual (x²-2)*Q(x).",
      "definitions": [
        "IRD11"
      ],
      "deps": [
        "IR005",
        "IR029",
        "IR009"
      ],
      "group": "Q",
      "id": "IR075",
      "independent_lean_receipt": null,
      "induction": "polynomial degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Quadratic polynomial remainder certificate",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For P=sum_alpha c_alpha*X^alpha, coordinate magnitudes<=R with R>=1 and coordinate differences<=delta imply |P(x)-P(y)|<=delta*sum_alpha |c_alpha|*|alpha|*R^(|alpha|-1), omitting degree-zero terms. Compute the bound from the coefficient table.",
      "definitions": [],
      "deps": [
        "IR009",
        "IR005",
        "IR004"
      ],
      "group": "A",
      "id": "IR076",
      "independent_lean_receipt": null,
      "induction": "monomial length and finite coefficient list",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite multivariate substitution error",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For d>=k, (d/dt)^k E_d(lambda*t)=lambda^k E_(d-k)(lambda*t); for d<k the formal derivative is zero. Derivative means the finite coefficient-list operation.",
      "definitions": [
        "IRD08"
      ],
      "deps": [
        "IR019",
        "IR005",
        "IR011"
      ],
      "group": "H",
      "id": "IR077",
      "independent_lean_receipt": null,
      "induction": "k and polynomial degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Finite Taylor derivative identity",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For M=7r, C_jk=L0^(-(M-k))*c_jk with rational denominator dividing720^M. Therefore M!*(720*L0)^M times the IR056 identity is polynomial; include the Taylor degree factorial to clear Taylor coefficients. Record every nonzero denominator and its lower bound.",
      "definitions": [
        "IRD21",
        "IRD22"
      ],
      "deps": [
        "IR055",
        "IR056",
        "IR018",
        "IR005"
      ],
      "group": "H",
      "id": "IR078",
      "independent_lean_receipt": null,
      "induction": "truncated inverse-product coefficients",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Denominator-cleared confluent identity",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Let A(z)=2*sum(j>=0,z^(2j+1)/(2j+1)) as finite coefficient tables. Formal exp(A) has F(0)=1 and (1-z²)F'=2F coefficientwise to each finite degree; composition only uses finitely many positive-degree terms.",
      "definitions": [
        "IRD07",
        "IRD08"
      ],
      "deps": [
        "IR005",
        "IR019",
        "IR021",
        "IR077"
      ],
      "group": "S",
      "id": "IR079",
      "independent_lean_receipt": null,
      "induction": "coefficient degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Formal atanh/exponential coefficient recurrence",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "The recurrence of IR079 uniquely determines coefficients and agrees with (1+z)/(1-z)=1+2*sum(j>=1,z^j). Prove by induction on the coefficient index, with positive integer division justified.",
      "definitions": [
        "IRD07",
        "IRD08"
      ],
      "deps": [
        "IR079",
        "IR003",
        "IR005"
      ],
      "group": "S",
      "id": "IR080",
      "independent_lean_receipt": null,
      "induction": "coefficient index",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Formal recurrence identifies rational series",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For z=1/3, construct finite truncation degrees making the difference between exp(A(z)), the finite formal composition and the rational-series truncation smaller than any dyadic error. Bound the outer exponential tail, inner atanh tail and positive omitted coefficient mass separately.",
      "definitions": [
        "IRD07",
        "IRD08"
      ],
      "deps": [
        "IR080",
        "IR017",
        "IR020",
        "IR010",
        "IR023",
        "IR012"
      ],
      "group": "S",
      "id": "IR081",
      "independent_lean_receipt": null,
      "induction": "explicit tail schedules",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Composition-tail bound at one third",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For P over Z, x,y in [1,2], |P(x)-P(y)|<=M_P*|x-y|, where M_P=1+sum(j>=1,j*abs(a_j)*2^(j-1)); zero/trailing-zero encodings handled.",
      "definitions": [
        "IRD25",
        "IRD26"
      ],
      "deps": [
        "IR009",
        "IR005",
        "IR026"
      ],
      "group": "T",
      "id": "TR001",
      "independent_lean_receipt": null,
      "induction": "degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 2,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Integer polynomial evaluation stability",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Under P(c)=0, construct the finite arithmetic data needed for Q(sqrt2,c), including a valid basis, multiplication and equality procedure; degree bounds derive from P, not an algebraicity oracle.",
      "definitions": [
        "IRD25"
      ],
      "deps": [
        "IR029",
        "IR044",
        "TR001"
      ],
      "group": "T",
      "id": "TR002",
      "independent_lean_receipt": null,
      "induction": "finite algebraic construction",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 2,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Coded algebraic extension presentations",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Prove explicit nonzero algebraic lower bounds using finite determinants/resultants and conjugate/root bounds from a coded presentation. Replace the special quadratic norm without importing classical analysis.",
      "definitions": [
        "IRD25"
      ],
      "deps": [
        "TR002",
        "IR044",
        "IR035"
      ],
      "group": "T",
      "id": "TR003",
      "independent_lean_receipt": null,
      "induction": "field degree",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 2,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "General denominator and norm separation",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Generalize the fixed seven-node proof to m=2h+3, N=q², n=N/(2hm), with uniform finite interpolation and height estimates.",
      "definitions": [],
      "deps": [
        "TR003",
        "IR043",
        "IR047",
        "IR054",
        "IR060",
        "IR064"
      ],
      "group": "T",
      "id": "TR004",
      "independent_lean_receipt": null,
      "induction": "m and h",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 2,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Variable-node auxiliary estimate",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Produce positive polynomial certificates, by a reviewed quantitative approximate-root construction or an implemented checked PA-to-HA transformation. Neither route is assumed available.",
      "definitions": [
        "IRD26"
      ],
      "deps": [
        "TR001",
        "TR002",
        "TR003",
        "TR004",
        "IR072"
      ],
      "group": "T",
      "id": "TR005",
      "independent_lean_receipt": null,
      "induction": "explicit certificate construction",
      "kind": "lemma",
      "method": "native-induction",
      "native_ha_receipt": null,
      "phase": 2,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Polynomial nonvanishing bridge",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "forall integer polynomial codes P. Nonzero(P) -> exists n,w. TransCert(P,n,w). Establish the fixed constant interpretation by IR027; no bounded-degree substitute.",
      "definitions": [
        "IRD26"
      ],
      "deps": [
        "TR005",
        "IR027"
      ],
      "group": "T",
      "id": "TR006",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "lemma",
      "method": "native-search",
      "native_ha_receipt": null,
      "phase": 2,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Full positive transcendence",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "For every dispatched lemma freeze exact hypotheses, binder order, arities and expanded HA AST hash. Proposed IRD names acquire reviewed existing/new definition identities only after hygienic expansion-equivalence tests. Reject circular definitions and a definition containing its desired theorem.",
      "definitions": [],
      "deps": [],
      "group": "E",
      "id": "ENG001",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "structural-check",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Contract and definition elaboration gate",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Map each reused result to the exact checked Alpha/Stable statement, dependency closure and first-admission evidence. Similar names, an ordinary Lean demo and source-only candidates do not discharge any IR obligation.",
      "definitions": [],
      "deps": [
        "ENG001"
      ],
      "group": "E",
      "id": "ENG002",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "structural-check",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Existing-premise audit",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Run bounded native ring/compact_arith/norm_num/search pilots; record original goal, exact premise allowlist, deterministic strategy, certificate size and fresh HA replay. No external proof or model calls are silently accepted.",
      "definitions": [],
      "deps": [
        "ENG001",
        "ENG002"
      ],
      "group": "E",
      "id": "ENG003",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "native-ring",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "routine",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Model-free native baseline",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Export only whitelisted elaborated obligations with natural-domain guards, exact integer/rational encoding, original target hash and checked-premise hashes. No real pow/log oracle, unproved induction schema or lossy denominator transformation.",
      "definitions": [],
      "deps": [
        "ENG001",
        "ENG002"
      ],
      "group": "E",
      "id": "ENG004",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "structural-check",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Guarded SMT/TPTP export",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Initially consume solver substitutions/rewrite hints through native proof generation. A success requires reconstruction of the original HA formula and fresh native checking. Unknown inference, clausification, Skolemization or arithmetic rule fails closed.",
      "definitions": [],
      "deps": [
        "ENG003",
        "ENG004"
      ],
      "group": "E",
      "id": "ENG005",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "certificate-reconstruction",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "External hint reconstruction",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Reject altered premises/targets, missing natural guards, swapped variables, forged unsat, unsupported proof steps, DNE, truncated logs and stale caches; independently check identical accepted native bundle bytes in Lean.",
      "definitions": [],
      "deps": [
        "ENG005"
      ],
      "group": "E",
      "id": "ENG006",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "structural-check",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Hostile replay and independent Lean",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "Wrap each native/solver worker in run_bounded with CPU,wall,RSS and output limits; hard total tranche deadline; no solver-internal process portfolios; checkpoint exact inputs, unknowns, solver hits, reconstructed proofs, genuine LLM tokens and fresh HA accepts separately.",
      "definitions": [],
      "deps": [
        "ENG003"
      ],
      "group": "E",
      "id": "ENG007",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "structural-check",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "high",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Bounded scheduler and accounting",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "IR072-74 are accepted in empty context by ordinary HA and independent Lean; every dependency is authenticated, definitions expanded, full quantified endpoint retained. Only then replace planning pages with canonical exact/defined proof explorers and seek Alpha promotion/deployment.",
      "definitions": [],
      "deps": [
        "IR072",
        "IR073",
        "IR074",
        "ENG006",
        "ENG007"
      ],
      "group": "E",
      "id": "ENG008",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "structural-check",
      "native_ha_receipt": null,
      "phase": 1,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Final irrationality closure and presentation",
      "worker_state": "blocked_on_contract_elaboration"
    },
    {
      "authority": "planning_only",
      "contract": "If direct perturbation fails its bounded pilot, separately implement negative translation plus Friedman A-translation on a tiny supported arithmetic proof calculus. Test induction, binders and eigenvariables; emit ordinary HA certificates. No Markov axiom or automatic arbitrary Lean import.",
      "definitions": [],
      "deps": [
        "ENG001",
        "ENG003"
      ],
      "group": "E",
      "id": "ENG009",
      "independent_lean_receipt": null,
      "induction": "none",
      "kind": "engineering",
      "method": "certificate-reconstruction",
      "native_ha_receipt": null,
      "phase": 0,
      "risk": "critical",
      "statement_ast_sha256": null,
      "status": "planned",
      "title": "Fallback proof-translation pilot (not primary route)",
      "worker_state": "blocked_on_contract_elaboration"
    }
  ],
  "parent_snapshots": {
    "campaign.json": "ed62081e992ca40e7e7788e0fbb8500a34bf94bbe0c75854616edce47811065f",
    "definitions.json": "32da2185fd21fb1d0b400404f9b832425a4c35e75be392a3f5b5f73f8464aebf",
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  },
  "pilot": [
    {
      "closes_parent": false,
      "contract": "Addition respects RatEq for two pairs of positive-denominator triples: clear denominators and emit the cross-multiplied polynomial identity.",
      "id": "P01",
      "method": "native-ring",
      "parent": "IR002",
      "required_negative_test": "Drop one positive-denominator guard or swap a numerator sign.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "For four arbitrary signed integers A,B,C,D, (AC+2BD)^2-2(AD+BC)^2=(A^2-2B^2)(C^2-2D^2), encoded as a subtraction-free natural equality.",
      "id": "P02",
      "method": "native-ring",
      "parent": "IR031",
      "required_negative_test": "Replace the coefficient 2 in the quadratic product by 3.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Power-difference induction STEP only: from witnessed e-th powers and their telescoping-sum identity derive the (e+1)-st identity using the sum recurrence. Freeze the exact induction hypothesis as a premise.",
      "id": "P03",
      "method": "native-ring",
      "parent": "IR009",
      "required_negative_test": "Omit the induction hypothesis or shift the final summand exponent.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Constant-coefficient BASE of formal exp(A): for the fixed positive-degree inner series with A_0=0, the coefficient of degree zero of the finite composition is 1.",
      "id": "P04",
      "method": "native-numeral",
      "parent": "IR079",
      "required_negative_test": "Allow a nonzero constant term in the inner series.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Recurrence STEP for k>=2 after f_k=f_(k-1)=2: justify the candidate f_(k+1)=2 in (k+1)f_(k+1)=2f_k+(k-1)f_(k-1). The k=0,1 boundaries stay separate parent obligations.",
      "id": "P05",
      "method": "native-ring",
      "parent": "IR080",
      "required_negative_test": "Use k instead of k+1 on the left-hand coefficient.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Single tail-contraction step: for x>=0, j>=0, j+1>=2x and t=x^j/j!>=0, the successor term x*t/(j+1)<=t/2. Clear strictly positive denominators and keep the product-order lemma explicit.",
      "id": "P06",
      "method": "native-order",
      "parent": "IR020",
      "required_negative_test": "Omit j+1>=2x and require a counterexample to be detected.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Two-frequency moment INSTANCE: M0=b0+b1, M1=b0*l0+b1*l1 imply M1+b0*l1=l1*M0+b0*l0. Signed values use coefficient-pair encoding; arbitrary N is not inferred.",
      "id": "P07",
      "method": "native-ring",
      "parent": "IR045",
      "required_negative_test": "Exchange b0 and b1 only on one side of the identity.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "First reciprocal-coefficient step for the fixed factor (d+w)^(-m), m>=1,d!=0: c0=d^(-m), c1=-m*d^(-m-1), so d*c1+m*c0=0. Powers and inverse witnesses are explicit.",
      "id": "P08",
      "method": "native-ring",
      "parent": "IR055",
      "required_negative_test": "Change the sign of c1 or remove the nonzero-denominator premise.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Finite confluent INSTANCE r=1, ell*=3, x_j=j*L0 (j<7), 1/4<=L0<=1/2: the degree-7 monomial functional equals 1. Generate its exact reciprocal coefficients, clear 7!*(720L0)^7 and replay the resulting identity; no universal r claim.",
      "id": "P09",
      "method": "native-ring",
      "parent": "IR056",
      "required_negative_test": "Give the selected node multiplicity 1 instead of 2.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Closed constant inequality 2^55*3^11*7^5<=2^88. Compute exact integers and generate a double-and-add arithmetic certificate, not a floating-point comparison.",
      "id": "P10",
      "method": "native-numeral",
      "parent": "IR064",
      "required_negative_test": "Lower the right exponent to 85; the resulting inequality is false.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Precision-bridge arithmetic: K,S,J>0 and e>=12KSJ imply 3/e<=1/(4KSJ). Introduce an explicit product witness V=KSJ, prove its positivity, clear denominators, then isolate the linear leaf e>=12V.",
      "id": "P11",
      "method": "native-order",
      "parent": "IR069",
      "required_negative_test": "Replace 12 by 8 and demand rejection or a rational counterexample.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    },
    {
      "closes_parent": false,
      "contract": "Fixed rational certificate INSTANCE a=3,b=2,n=6: generate the specified CApprox trace and prove |2*u_6-3|>4*2^(-6) in the unchanged kernel. This instance does not prove accuracy or universal irrationality.",
      "id": "P12",
      "method": "native-numeral",
      "parent": "IR071",
      "required_negative_test": "Mutate one approximation trace entry while retaining the claimed result.",
      "statement_ast_sha256": null,
      "status": "blocked_on_contract_and_premise_elaboration"
    }
  ],
  "pilot_policy": {
    "count_as": "child-leaf checks only, never universal parent closure",
    "elaboration_gates": [
      "ENG001",
      "ENG002"
    ],
    "external_inference_acceptance": "Only fresh reconstruction of the original HA target counts; unavailable tools are recorded, not installed implicitly.",
    "paired_runs": "Identical frozen formulas: native-only, then native plus guarded solver hints; both runs share the per-leaf budget.",
    "repair_budget": "One changed-strategy repair, within the original reservation; no unchanged retry."
  },
  "schema": "sqrt2-power-ha-campaign-plan-v1",
  "slug": "sqrt2-power",
  "sources": [
    {
      "id": "SRC1",
      "title": "Friedman: Gelfond-Schneider and the conditional PA-to-HA route (2000)",
      "url": "https://fomarchive.ugent.be/2000-June/004116.html"
    },
    {
      "id": "SRC2",
      "title": "Selinger: Friedman's A-translation (1992)",
      "url": "https://www.mathstat.dal.ca/~selinger/papers/friedman.pdf"
    },
    {
      "id": "SRC3",
      "title": "Karatarakis and Wiedijk: Lean Gelfond-Schneider formalization (2026)",
      "url": "https://arxiv.org/html/2603.24823v1"
    },
    {
      "id": "SRC4",
      "title": "Z3: proof logs and incomplete big-step hints",
      "url": "https://microsoft.github.io/z3guide/programming/Proof%20Logs/"
    },
    {
      "id": "SRC5",
      "title": "E: proof objects and checker limitations",
      "url": "https://github.com/eprover/eprover"
    },
    {
      "id": "SRC6",
      "title": "Vampire: supported TPTP proof output",
      "url": "https://github.com/vprover/vampire/releases"
    }
  ],
  "title": "Irrationality of (√2)^(√2)",
  "verified_new_theorem_count": 0
}