{
  "status": "rejected",
  "factorization_verified": false,
  "multiply_back_matches": true,
  "leading_coefficient_matches": true,
  "all_factors_irreducible": false,
  "reconstructed_polynomial": [
    2,
    3,
    1
  ],
  "factor_checks": [
    {
      "polynomial": [
        2,
        3,
        1
      ],
      "multiplicity": 1,
      "irreducible": false,
      "degree": 2,
      "frobenius_final_residual": [
        0
      ],
      "gcd_checks": [
        {
          "degree_prime_divisor": 2,
          "frobenius_iterations": 1,
          "gcd": [
            2,
            3,
            1
          ],
          "coprime": false
        }
      ]
    }
  ],
  "work_charged": 46,
  "limits": {
    "prime_max": 2147483647,
    "degree_max": 64,
    "work_limit": 2000000
  },
  "scope": "Conventional exact finite-field checks; no source large-characteristic backend or proof acceptance"
}