{
  "catalog_sha256_by_recorded_version": {
    "v28": "897410581b66552c7f01f4b1266de887e52b3198b1ff2d2ac5135ab694d467e9"
  },
  "per_theorem": [
    {
      "name": "natural_mul_swap_right_tail",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0001"
    },
    {
      "name": "signed_integer_floor_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0002"
    },
    {
      "name": "signed_integer_floor_quotient_transport",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0003"
    },
    {
      "name": "signed_integer_canonical_floor_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0004"
    },
    {
      "name": "signed_code_floor_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0005"
    },
    {
      "name": "gaussian_signed_square_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0006"
    },
    {
      "name": "gaussian_signed_square_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0007"
    },
    {
      "name": "gaussian_signed_square_negated",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0008"
    },
    {
      "name": "gaussian_signed_square_integer_transport",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0009"
    },
    {
      "name": "gaussian_signed_product_square_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI000A"
    },
    {
      "name": "gaussian_signed_product_square_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI000B"
    },
    {
      "name": "gaussian_signed_product_square_compensation",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI000C"
    },
    {
      "name": "gaussian_signed_square_product",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI000D"
    },
    {
      "name": "gaussian_signed_sum_square_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI000E"
    },
    {
      "name": "gaussian_signed_sum_square_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI000F"
    },
    {
      "name": "gaussian_signed_square_sum_compensation",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0010"
    },
    {
      "name": "gaussian_signed_square_difference_compensation",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0011"
    },
    {
      "name": "gaussian_signed_norm_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0012"
    },
    {
      "name": "gaussian_signed_norm_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0013"
    },
    {
      "name": "gaussian_signed_product_interchange_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0014"
    },
    {
      "name": "gaussian_signed_product_interchange_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0015"
    },
    {
      "name": "gaussian_signed_product_commutative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0016"
    },
    {
      "name": "gaussian_signed_product_shuffle",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0017"
    },
    {
      "name": "gaussian_signed_product_cross_interchange",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0018"
    },
    {
      "name": "gaussian_signed_square_lagrange",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0019"
    },
    {
      "name": "gaussian_signed_norm_product",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI001A"
    },
    {
      "name": "gaussian_signed_norm_integer_transport",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI001B"
    },
    {
      "name": "gaussian_signed_norm_conjugate",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI001C"
    },
    {
      "name": "gaussian_signed_square_zero_iff",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI001D"
    },
    {
      "name": "gaussian_signed_norm_nonzero",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI001E"
    },
    {
      "name": "gaussian_signed_square_scaled",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI001F"
    },
    {
      "name": "gaussian_product_associate_real_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0020"
    },
    {
      "name": "gaussian_product_associate_real_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0021"
    },
    {
      "name": "gaussian_product_associate_imaginary_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0022"
    },
    {
      "name": "gaussian_product_associate_imaginary_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0023"
    },
    {
      "name": "gaussian_product_difference_real_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0024"
    },
    {
      "name": "gaussian_product_difference_real_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0025"
    },
    {
      "name": "gaussian_product_difference_imaginary_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0026"
    },
    {
      "name": "gaussian_product_difference_imaginary_negative",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0027"
    },
    {
      "name": "gaussian_product_associate",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0028"
    },
    {
      "name": "gaussian_product_difference",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0029"
    },
    {
      "name": "gaussian_equal_reflexive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI002A"
    },
    {
      "name": "gaussian_equal_symmetric",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI002B"
    },
    {
      "name": "gaussian_equal_transitive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI002C"
    },
    {
      "name": "gaussian_product_integer_congruence",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI002D"
    },
    {
      "name": "gaussian_difference_integer_congruence",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI002E"
    },
    {
      "name": "gaussian_signed_norm_balance",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI002F"
    },
    {
      "name": "gaussian_conjugate_product_is_norm",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0030"
    },
    {
      "name": "gaussian_natural_scalar_product",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0031"
    },
    {
      "name": "gaussian_adjoint_product_is_norm_scale",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0032"
    },
    {
      "name": "gaussian_residual_conjugate_identity",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0033"
    },
    {
      "name": "gaussian_difference_reconstructs_dividend",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0034"
    },
    {
      "name": "gaussian_nonzero_natural_positive",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0035"
    },
    {
      "name": "gaussian_double_square_strict",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0036"
    },
    {
      "name": "gaussian_half_double_square_strict",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0037"
    },
    {
      "name": "gaussian_two_half_squares_strict",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0038"
    },
    {
      "name": "gaussian_nearest_signed_quotient_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0039"
    },
    {
      "name": "gaussian_signed_euclidean_division_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI003A"
    },
    {
      "name": "gaussian_signed_balance_integer_transport",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI003B"
    },
    {
      "name": "gaussian_signed_balance_same_code",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI003C"
    },
    {
      "name": "gaussian_decode_from_signed_codes",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI003D"
    },
    {
      "name": "gaussian_decode_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI003E"
    },
    {
      "name": "gaussian_representation_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI003F"
    },
    {
      "name": "gaussian_representation_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0040"
    },
    {
      "name": "gaussian_representation_integer_transport",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0041"
    },
    {
      "name": "gaussian_representation_equal",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0042"
    },
    {
      "name": "gaussian_representation_decode",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0043"
    },
    {
      "name": "gaussian_decode_representation",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0044"
    },
    {
      "name": "gaussian_representation_is_gaussian",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0045"
    },
    {
      "name": "gaussian_pair_zero_codes",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0046"
    },
    {
      "name": "gaussian_representation_zero_iff",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0047"
    },
    {
      "name": "gaussian_decode_zero_iff",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0048"
    },
    {
      "name": "gaussian_signed_add_of_balances",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0049"
    },
    {
      "name": "gaussian_signed_add_to_balance",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI004A"
    },
    {
      "name": "gaussian_signed_mul_of_balances",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI004B"
    },
    {
      "name": "gaussian_signed_mul_to_balance",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI004C"
    },
    {
      "name": "gaussian_norm_of_representation",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI004D"
    },
    {
      "name": "gaussian_norm_for_representation",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI004E"
    },
    {
      "name": "gaussian_norm_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI004F"
    },
    {
      "name": "gaussian_norm_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0050"
    },
    {
      "name": "gaussian_norm_exists_unique",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0051"
    },
    {
      "name": "gaussian_sum_integer_congruence",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0052"
    },
    {
      "name": "gaussian_add_of_representations",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0053"
    },
    {
      "name": "gaussian_add_for_representations",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0054"
    },
    {
      "name": "gaussian_add_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0055"
    },
    {
      "name": "gaussian_add_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0056"
    },
    {
      "name": "gaussian_multiply_of_representations",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0057"
    },
    {
      "name": "gaussian_multiply_for_representations",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0058"
    },
    {
      "name": "gaussian_multiply_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI0059"
    },
    {
      "name": "gaussian_multiply_functional",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI005A"
    },
    {
      "name": "gaussian_norm_multiply",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI005B"
    },
    {
      "name": "gaussian_division_remainder_of_representations",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI005C"
    },
    {
      "name": "gaussian_euclidean_division_exists",
      "recorded_authority": {
        "admitted_to_alpha": true,
        "admitted_to_stable": false,
        "alpha_checked_use": true,
        "alpha_evidence": "alpha_closed",
        "checked_use": true,
        "enrolled_in_alpha": true,
        "stable_member": false
      },
      "recorded_first_version": "v28",
      "tag": "GI005D"
    }
  ],
  "policy": "preserve_recorded_first_admission_without_inferring_it_from_current_or_proof_editions",
  "schema": "peano-lab-historical-first-admission-v1",
  "source_corpus": {
    "bytes": 2159283,
    "path": "book/_static/constructive-lower-layer-explorer-v30/gaussian-integers/api/corpus.json",
    "sha256": "2485862cd60e264d8ca4d974e416f1ba99fc694f65eb56df72ac852c43702815"
  },
  "source_corpus_fields": {
    "alpha_first_enrolled_version": "v28",
    "alpha_first_enrollment_catalog_sha256": "897410581b66552c7f01f4b1266de887e52b3198b1ff2d2ac5135ab694d467e9"
  },
  "source_family_fields": {},
  "source_manifest": {
    "bytes": 98859,
    "path": "book/_static/constructive-lower-layer-explorer-v30/manifest.json",
    "sha256": "6a40a3ec03840ad8ae73a6a29b594bd04d666a2aeb251a5f07fbfff2fd85bda2"
  },
  "source_manifest_fields": {
    "alpha_first_enrolled_version": "v28",
    "first_enrollment_catalog_sha256": "897410581b66552c7f01f4b1266de887e52b3198b1ff2d2ac5135ab694d467e9"
  }
}
