{
  "status": "verified",
  "factorization_verified": true,
  "multiply_back_matches": true,
  "leading_coefficient_matches": true,
  "all_factors_irreducible": true,
  "reconstructed_polynomial": [
    2,
    4,
    2
  ],
  "factor_checks": [
    {
      "polynomial": [
        1,
        1
      ],
      "multiplicity": 2,
      "irreducible": true,
      "degree": 1,
      "frobenius_final_residual": [
        0
      ],
      "gcd_checks": []
    }
  ],
  "work_charged": 13,
  "limits": {
    "prime_max": 2147483647,
    "degree_max": 64,
    "work_limit": 2000000
  },
  "scope": "Conventional exact finite-field checks; no source large-characteristic backend or proof acceptance"
}