{
  "scope": "Exact illustrative-example checks, not a new Lean verification or theorem census.",
  "python_version": "3.12.14",
  "sympy_version": "1.14.0",
  "script_sha256": "bb7809b2c40f79def2ef2bf1983e17bf067893948e077a8d766de1c2dc88df52",
  "status": "PASS",
  "check_count": 46,
  "checks": [
    {
      "name": "local_points_order_three",
      "status": "PASS",
      "detail": {
        "candidate_count": 625,
        "accepted_count": 5,
        "accepted": [
          [
            0,
            0,
            0,
            0
          ],
          [
            0,
            1,
            0,
            1
          ],
          [
            0,
            2,
            0,
            2
          ],
          [
            0,
            3,
            0,
            3
          ],
          [
            0,
            4,
            0,
            4
          ]
        ]
      }
    },
    {
      "name": "local_points_order_two",
      "status": "PASS",
      "detail": {
        "candidate_count": 25,
        "accepted_count": 5,
        "image_of_order_three": [
          [
            0,
            0
          ]
        ],
        "nonzero_tangent_directions_with_no_lift": 4
      }
    },
    {
      "name": "quotient_monomial_window",
      "status": "PASS",
      "detail": {
        "window_total_degree_less_than": 6,
        "shown": 21,
        "surviving_O_basis": [
          [
            0,
            0
          ],
          [
            1,
            0
          ]
        ]
      }
    },
    {
      "name": "adic_prefix_compatibility",
      "status": "PASS",
      "detail": [
        {
          "n": 1,
          "modulus": 5,
          "a": 1,
          "b": 1,
          "ring_cardinality": 25
        },
        {
          "n": 2,
          "modulus": 25,
          "a": 11,
          "b": 16,
          "ring_cardinality": 625
        },
        {
          "n": 3,
          "modulus": 125,
          "a": 11,
          "b": 16,
          "ring_cardinality": 15625
        },
        {
          "n": 4,
          "modulus": 625,
          "a": 11,
          "b": 266,
          "ring_cardinality": 390625
        },
        {
          "n": 5,
          "modulus": 3125,
          "a": 1261,
          "b": 2766,
          "ring_cardinality": 9765625
        },
        {
          "n": 6,
          "modulus": 15625,
          "a": 4386,
          "b": 5891,
          "ring_cardinality": 244140625
        }
      ]
    },
    {
      "name": "fitting_matrix_index_0",
      "status": "PASS",
      "detail": {
        "generators": [
          "x*y"
        ]
      }
    },
    {
      "name": "presentation_stabilization_index_0",
      "status": "PASS",
      "detail": "Explicit diag(x,y) versus diag(x,y,1), not a proof of general presentation independence."
    },
    {
      "name": "fitting_matrix_index_1",
      "status": "PASS",
      "detail": {
        "generators": [
          "x",
          "0",
          "0",
          "y"
        ]
      }
    },
    {
      "name": "presentation_stabilization_index_1",
      "status": "PASS",
      "detail": "Explicit diag(x,y) versus diag(x,y,1), not a proof of general presentation independence."
    },
    {
      "name": "fitting_matrix_index_2",
      "status": "PASS",
      "detail": {
        "generators": [
          "1"
        ]
      }
    },
    {
      "name": "presentation_stabilization_index_2",
      "status": "PASS",
      "detail": "Explicit diag(x,y) versus diag(x,y,1), not a proof of general presentation independence."
    },
    {
      "name": "nilpotent_fitting_ideals",
      "status": "PASS",
      "detail": {
        "F0": "(x^2 y)",
        "F1": "(x^2,y)"
      }
    },
    {
      "name": "fiber_rank_1_1",
      "status": "PASS",
      "detail": {
        "point": [
          1,
          1
        ],
        "fiber_dimension": 0
      }
    },
    {
      "name": "fiber_rank_0_1",
      "status": "PASS",
      "detail": {
        "point": [
          0,
          1
        ],
        "fiber_dimension": 1
      }
    },
    {
      "name": "fiber_rank_1_0",
      "status": "PASS",
      "detail": {
        "point": [
          1,
          0
        ],
        "fiber_dimension": 1
      }
    },
    {
      "name": "fiber_rank_0_0",
      "status": "PASS",
      "detail": {
        "point": [
          0,
          0
        ],
        "fiber_dimension": 2
      }
    },
    {
      "name": "diagonal_base_change_0",
      "status": "PASS",
      "detail": {
        "expected": [
          "t**2"
        ]
      }
    },
    {
      "name": "diagonal_base_change_1",
      "status": "PASS",
      "detail": {
        "expected": [
          "t"
        ]
      }
    },
    {
      "name": "diagonal_base_change_2",
      "status": "PASS",
      "detail": {
        "expected": [
          "1"
        ]
      }
    },
    {
      "name": "coordinate_change_invertible",
      "status": "PASS",
      "detail": "Over characteristic not equal to 2; the geometric plate uses real coordinates."
    },
    {
      "name": "coordinate_change_fitting",
      "status": "PASS",
      "detail": {
        "F0": "(a^2-b^2)",
        "F1": "(a,b)"
      }
    },
    {
      "name": "CRT_polynomial_congruences",
      "status": "PASS",
      "detail": {
        "p_plus": "-3*z**4/16 - z**3/4 + 3*z**2/8 + 3*z/4 + 5/16",
        "modulus": "z**5 + z**4 - 2*z**3 - 2*z**2 + z + 1"
      }
    },
    {
      "name": "CRT_matrix_projectors",
      "status": "PASS",
      "detail": {
        "ranks": [
          2,
          3
        ],
        "traces": [
          "2",
          "3"
        ]
      }
    },
    {
      "name": "ordinary_vs_generalized",
      "status": "PASS",
      "detail": {
        "ordinary": [
          1,
          1
        ],
        "generalized": [
          2,
          3
        ]
      }
    },
    {
      "name": "packet_residue_fibers",
      "status": "PASS",
      "detail": "Regular local packet dimensions 2 and 3, residue fibers each dimension 1."
    },
    {
      "name": "empty_packet_example",
      "status": "PASS",
      "detail": "The supplied T-module T_+ is not faithful on the second factor."
    },
    {
      "name": "dyadic_idempotents",
      "status": "PASS",
      "detail": [
        [
          0,
          0
        ],
        [
          1,
          0
        ]
      ]
    },
    {
      "name": "dyadic_involution",
      "status": "PASS",
      "detail": "Multiplication by g=1+d has g^2=1 over F_2 and a nonzero nilpotent part."
    },
    {
      "name": "trace_not_occupancy_in_characteristic_two",
      "status": "PASS",
      "detail": {
        "idempotent": "I_2",
        "rank_over_F2": 2,
        "trace_over_F2": 0
      }
    },
    {
      "name": "stable_core_identities",
      "status": "PASS",
      "detail": {
        "P_power_image_dimensions": [
          3,
          1,
          1,
          1,
          1
        ],
        "N_power_image_dimensions": [
          3,
          2,
          1,
          0,
          0
        ]
      }
    },
    {
      "name": "fixed_carrier_nested_projectors",
      "status": "PASS",
      "detail": {
        "dimensions": [
          5,
          4,
          4,
          2,
          1,
          1,
          1,
          1
        ],
        "a_plateau_precedes_a_later_drop": true,
        "definition_after_level_5": "constant projector onto e_1"
      }
    },
    {
      "name": "derived_fiber_dimensions",
      "status": "PASS",
      "detail": "C=[k[t] --t--> k[t]] in degrees 0,1; all a != 0 give an isomorphism."
    },
    {
      "name": "S3_group_relations_F7",
      "status": "PASS",
      "detail": "Exact defining relations modulo 7."
    },
    {
      "name": "S3_projector_pairings_F7",
      "status": "PASS",
      "detail": {
        "pairings_mod_7": [
          3,
          6
        ]
      }
    },
    {
      "name": "S3_projector_idempotence_F7",
      "status": "PASS",
      "detail": "Printed canonical projectors are idempotent."
    },
    {
      "name": "S3_canonical_formula_F7",
      "status": "PASS",
      "detail": "Inverses of 2-4 and 1-(-1) are 3 and 4 in F7."
    },
    {
      "name": "S3_adjoint_basis_F7",
      "status": "PASS",
      "detail": "Columns Z,A,B have determinant 3 modulo 7."
    },
    {
      "name": "S3_eigenvalue_polynomials_F7",
      "status": "PASS",
      "detail": "Characteristic polynomials split as printed."
    },
    {
      "name": "augmentation_binomial_relations_F2",
      "status": "PASS",
      "detail": "C4 x C2 relations in F2."
    },
    {
      "name": "augmentation_basis_and_nilpotence",
      "status": "PASS",
      "detail": {
        "basis_exponents": [
          [
            0,
            0
          ],
          [
            1,
            0
          ],
          [
            2,
            0
          ],
          [
            3,
            0
          ],
          [
            0,
            1
          ],
          [
            1,
            1
          ],
          [
            2,
            1
          ],
          [
            3,
            1
          ]
        ],
        "nilpotence_bound": 5
      }
    },
    {
      "name": "conjugate_involution_frame",
      "status": "PASS",
      "detail": "Both frames satisfy A^2=I."
    },
    {
      "name": "frame_reduction_mismatch",
      "status": "PASS",
      "detail": "Compatible conjugacy classes need not give compatible arbitrary frames."
    },
    {
      "name": "compatible_diagonal_representatives",
      "status": "PASS",
      "detail": "Prefixes checked through level 6; the all-level formula is reduction of one integral D."
    },
    {
      "name": "involution_equations",
      "status": "PASS",
      "detail": "Four exact entries of A^2-I."
    },
    {
      "name": "frame_sensitive_entry",
      "status": "PASS",
      "detail": "a12=0 is not invariant under admissible change of frame."
    },
    {
      "name": "trace_separator_exact_solution",
      "status": "PASS",
      "detail": {
        "determinant": -2,
        "multiplicities": [
          3,
          2
        ]
      }
    },
    {
      "name": "trace_separator_dyadic_failure",
      "status": "PASS",
      "detail": "The same sample rows merge in characteristic two."
    }
  ],
  "limits": [
    "Finite arithmetic enumerations are exhaustive only for their stated finite models.",
    "Uniform algebraic conclusions and infinite-limit claims have explicit arguments in the appendix.",
    "No test verifies external arithmetic existence, classicality, or automorphy inputs.",
    "No new examples have been formalized in Lean by this editorial release."
  ]
}