{
  "input_record_sha256": "b18cd835b41967fb6621f88fae408d15e8d5c26b448b6633ffb13039e5b35e68",
  "source_connection": {
    "family": "169",
    "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
    "source_proof_verification": "not_run"
  },
  "formal_program_verification": "not_run",
  "arithmetic": "exact_integer_and_rational",
  "vertices": 3,
  "edges": [
    [
      0,
      1
    ],
    [
      1,
      2
    ]
  ],
  "colors": 3,
  "limits": {
    "vertices": 6,
    "work_budget": 2000000,
    "wall_time_deadline": "none"
  },
  "work_unit_definition": "Color assignments/edge probes, polynomial product terms, coefficient comparisons and rational elimination operations; not bit operations or elapsed time.",
  "status": "complete",
  "work_units": 215,
  "proper_colorings_with_n_colors": 12,
  "elementary_coefficients": [
    {
      "partition": [
        3
      ],
      "q_coefficients": [
        "1",
        "1",
        "1"
      ]
    },
    {
      "partition": [
        2,
        1
      ],
      "q_coefficients": [
        "0",
        "1",
        "0"
      ]
    }
  ],
  "monomial_coefficients": [
    {
      "partition": [
        2,
        1
      ],
      "q_coefficients": [
        0,
        1,
        0
      ]
    },
    {
      "partition": [
        1,
        1,
        1
      ],
      "q_coefficients": [
        1,
        4,
        1
      ]
    }
  ],
  "coefficients_nonnegative_integers": true,
  "complete_finite_polynomial_reconstructed": true,
  "eligible_permutations": 4,
  "witness_status": "finite_polynomial_matches",
  "witness_differences": [],
  "interpretation": "Exact degree-n polynomial in n colors and conventional basis conversion. Supplied witness status checks this finite polynomial only; no source packet algorithm, all-r formal proof, uniform constructive witness, geometric basis or polynomial runtime is certified."
}