{
  "groups": {
    "canonical_readouts": {
      "example_field": "p(z)=3-2z",
      "fractional_example": true,
      "outer_readings": [
        [
          "5/1",
          "2/1",
          "2/1",
          "0/1"
        ],
        [
          "1/1",
          "-2/1",
          "-2/1",
          "0/1"
        ]
      ],
      "rational_independence": {
        "cited_degree_of_Q_cos": 172800,
        "classical_formula": "For m >= 3, [Q(cos(2*pi/m)):Q] = phi(m)/2. Not reproved here.",
        "conclusion": "sin(pi/1296000) is not in Q(phi). The set {1, phi, s, phi*s} is a Q-basis. s*s leaves that span.",
        "euler_totient": 345600,
        "m": 1296000
      },
      "recovered": [
        [
          "3/1",
          "0/1"
        ],
        [
          "-2/1",
          "0/1"
        ]
      ],
      "rejected_records": 5,
      "symbolic_inverse": true
    },
    "grid_transfer": {
      "basis_recoveries": 9,
      "composition": true,
      "constants_preserved": true,
      "gram_entries_each": 81,
      "grids": 3,
      "harmonic_degree": 2,
      "higher_frequency": "not enabled",
      "nodes_each": 12,
      "round_trip": true
    },
    "integer_layer": {
      "collision_inputs": [
        [
          4,
          7
        ],
        [
          5,
          6
        ]
      ],
      "serialized_bytes": [
        77,
        77
      ],
      "shared_rho": [
        2
      ],
      "shared_y": [
        2
      ],
      "signed_recoveries": 4,
      "smith_example_diagonal": [
        2,
        4
      ],
      "storage_note": "The serialized witness is sufficient. Its byte length is not claimed to be optimal.",
      "witnesses": [
        [
          7
        ],
        [
          6
        ]
      ]
    }
  },
  "limits": [
    "Not a proof-assistant kernel certificate.",
    "The cyclotomic degree formula is cited, not reproved.",
    "The canonical sine is not evaluated.",
    "Witness byte length is not an optimality claim.",
    "Different subdivision frequencies are not enabled.",
    "Items 4, 5, and 6 of the directive are not in this release."
  ],
  "release": "supplement-1",
  "status": "PASS"
}