{
  "origin": "coordinator_exact_symbolic_checks_of_user_supplied_Astra_claim_not_independent_model_or_formal_certificate",
  "source_sha256": "e6f3ee5af078764b1750ea6a8cdbc8c1d9577ef6d14d0bc638830f385d839db8",
  "checker_sha256": "a0df3c7b0e25ce3d2aa1c7a1821d23d702f5de50dfb73e94ac89671a70d44711",
  "sympy_version": "1.14.0",
  "matrix": [
    [
      "2",
      "2/3",
      "0"
    ],
    [
      "0",
      "1",
      "0"
    ],
    [
      "0",
      "0",
      "1/2"
    ]
  ],
  "dual_matrix": [
    [
      "1/2",
      "0",
      "0"
    ],
    [
      "-1/3",
      "1",
      "0"
    ],
    [
      "0",
      "0",
      "2"
    ]
  ],
  "determinant": "1",
  "hodge_exterior_square_identity_verified": true,
  "fixed_vector": "2 e1",
  "all_integer_vector_argument": "See counterexample.md; q=exp(L/6)>=4 for L>=10. Coordinate/disibility cases cover every nonzero vector.",
  "minima_for_L_ge_10": {
    "positive_standard": "(1/2) exp(-L/6)",
    "positive_dual": "(3/2) exp(-L/3)",
    "negative_standard": "2 exp(-L/3)",
    "negative_dual": "exp(-L/6)"
  },
  "finite_box_sanity_checks": {
    "coordinate_range": [
      -6,
      6
    ],
    "nonzero_vectors_per_box": 2196,
    "checks": [
      {
        "q": "4",
        "exact_minima_euclidean_and_sup": [
          "1/8",
          "3/32",
          "1/8",
          "1/4"
        ]
      },
      {
        "q": "8",
        "exact_minima_euclidean_and_sup": [
          "1/16",
          "3/128",
          "1/32",
          "1/8"
        ]
      }
    ]
  },
  "thickness_margin_multiple": "at least 3/2 for both signs",
  "retained_set_failure": {
    "delta1": "1/100000",
    "epsilon_upper_bound": "1/1000",
    "positive_exponent_gap_lower_bound": "79997/12000000000",
    "conclusion": "Every point is removed for all sufficiently large t; F is empty."
  },
  "general_family": "Critical coefficients c and Q/c; can exceed every fixed normalization constant.",
  "curve_rescaled_quadratic_remainder": "1/4",
  "limitations": [
    "Exact script uses v6; publication separately compares official journal passages.",
    "Branch proofs and fixed-vector measure obstruction are supplied in the accompanying note.",
    "No amended theorem or curve corollary is certified by this script."
  ]
}