{
  "determinant_mod_11": 2,
  "local_matrix": [
    [
      1,
      2
    ],
    [
      1,
      4
    ]
  ],
  "local_results": [
    {
      "P_orbit_equals_all_points": true,
      "Q_discrete_log_base_P": 244,
      "Q_norm_coordinate": 2,
      "a_ell": 24,
      "ell": 397,
      "group_order": 374,
      "independent_counts_agree": true,
      "multiplied_P": [
        281,
        236
      ],
      "multiplied_Q": [
        11,
        334
      ],
      "order_of_P": 374,
      "order_of_multiplied_P": 11,
      "prime_to_11_multiplier": 34
    },
    {
      "P_orbit_equals_all_points": true,
      "Q_discrete_log_base_P": 356,
      "Q_norm_coordinate": 4,
      "a_ell": -53,
      "ell": 991,
      "group_order": 1045,
      "independent_counts_agree": true,
      "multiplied_P": [
        39,
        97
      ],
      "multiplied_Q": [
        865,
        243
      ],
      "order_of_P": 1045,
      "order_of_multiplied_P": 11,
      "prime_to_11_multiplier": 95
    }
  ],
  "minimal_invariants": {
    "b2": 4,
    "b4": -4,
    "b6": 1,
    "b8": -3,
    "c4": 112,
    "discriminant": 389,
    "discriminant_is_prime": true
  },
  "norm_kernel_dimensions_on_span_PQ": [
    2,
    1,
    1,
    0
  ],
  "original_points": {
    "P": [
      0,
      0
    ],
    "Q": [
      1,
      0
    ]
  },
  "prior_source_sha256": "2d911f09dd5d19da402dd6a34ae7b3c26e1179df3743fa9fc9e723819fd6fcfe",
  "residual_irreducibility_witness": {
    "a_2": -2,
    "characteristic_polynomial_mod_11": [
      1,
      2,
      2
    ],
    "discriminant_mod_11": 7,
    "frobenius_prime": 2,
    "note": "Transvection and subgroup arguments are proved in the manuscript, not computed here.",
    "roots_mod_11": [],
    "square_residues_mod_11": [
      0,
      1,
      3,
      4,
      5,
      9
    ]
  },
  "schema": "kurihara-prior-input-replay-v1",
  "scope": "Exact curve and local-point inputs; canonical primitivity and Kim consequences are theorem applications.",
  "short_model_points": {
    "P": [
      12,
      108
    ],
    "Q": [
      48,
      108
    ]
  },
  "small_point_counts": {
    "11": 16,
    "2": 5,
    "5": 9
  },
  "verdict": "PASS"
}