{
  "all_red": true,
  "consumed_sha256": "41731c987fade25c26b205fb02c809a2b75461ddeae852869ad61aab2804e114",
  "controls_status": "PASS",
  "counts": {
    "exact/not_refuted": 37904,
    "null-dag/PASS": 281,
    "null/PASS": 41,
    "real-dag/PASS": 482,
    "real/PASS": 11,
    "sub/PASS": 1590,
    "super/not_refuted": 405540,
    "tree/PASS": 1099,
    "tu/PASS": 1760
  },
  "failures": [],
  "identities": {
    "cofactor": 312,
    "dag_row": 267276,
    "dag_target": 4578,
    "sos": 450,
    "tree_discriminant": 33000,
    "tree_relation": 96300,
    "tree_rowspace": 96300,
    "tree_unit_ratio": 23706
  },
  "identities_per_point": 86987,
  "max_input_polynomial_degree": 159,
  "nonidentities_not_checked": [
    "Sturm root count",
    "selected-root signs/irreducibility",
    "TU forcing lemmas",
    "sub-pointer containment/dependencies"
  ],
  "points_per_prime": 3,
  "polynomial_identity_degree_bound": 318,
  "primes": [
    "2305843009213693951",
    "170141183460469231731687303715884105727"
  ],
  "probability_caveat": "Schwartz-Zippel applies only if the rational difference remains a nonzero polynomial modulo a chosen prime; deliberate prime-multiple discrepancies are outside this fixed-prime control",
  "red_controls": [
    {
      "code": "cofactor_identity",
      "expected_codes": [
        "cofactor_identity"
      ],
      "g6": "J??H`KZxEo?",
      "name": "null: cofactor coefficient +1",
      "positive_pass": true,
      "reason": "cofactor identity fails",
      "red": true
    },
    {
      "code": "cofactor_identity",
      "expected_codes": [
        "cofactor_identity"
      ],
      "g6": "J??H`KZxEo?",
      "name": "null: cofactor term removed",
      "positive_pass": true,
      "reason": "cofactor identity fails",
      "red": true
    },
    {
      "code": "frame",
      "expected_codes": [
        "frame"
      ],
      "g6": "J??H`KZxEo?",
      "name": "null: invalid frame",
      "positive_pass": true,
      "reason": "frame is not an actual edge",
      "red": true
    },
    {
      "code": "row_identity",
      "expected_codes": [
        "row_identity"
      ],
      "g6": "J??XOdcqTb?",
      "name": "null-dag: row coefficient perturbed",
      "positive_pass": true,
      "reason": "row 0 identity fails",
      "red": true
    },
    {
      "code": "row_identity",
      "expected_codes": [
        "row_identity"
      ],
      "g6": "J??XOdcqTb?",
      "name": "null-dag: final cofactors removed",
      "positive_pass": true,
      "reason": "row 63 identity fails",
      "red": true
    },
    {
      "code": "frame",
      "expected_codes": [
        "frame"
      ],
      "g6": "J??XOdcqTb?",
      "name": "null-dag: invalid frame",
      "positive_pass": true,
      "reason": "frame is not an actual edge",
      "red": true
    },
    {
      "code": "last_target",
      "expected_codes": [
        "last_target"
      ],
      "g6": "J??XOdcqTb?",
      "name": "null-dag: last row removed",
      "positive_pass": true,
      "reason": "last row is not the required target",
      "red": true
    },
    {
      "code": "cofactor_identity",
      "expected_codes": [
        "cofactor_identity"
      ],
      "g6": "J?aPROSOj`_",
      "name": "real: cofactor coefficient +1",
      "positive_pass": true,
      "reason": "cofactor identity fails",
      "red": true
    },
    {
      "code": "cofactor_identity",
      "expected_codes": [
        "cofactor_identity"
      ],
      "g6": "J?aPROSOj`_",
      "name": "real: cofactor term removed",
      "positive_pass": true,
      "reason": "cofactor identity fails",
      "red": true
    },
    {
      "code": "frame",
      "expected_codes": [
        "frame"
      ],
      "g6": "J?aPROSOj`_",
      "name": "real: invalid frame",
      "positive_pass": true,
      "reason": "frame is not an actual edge",
      "red": true
    },
    {
      "code": "row_identity",
      "expected_codes": [
        "row_identity"
      ],
      "g6": "J??QIOwi\\k?",
      "name": "real-dag: row coefficient perturbed",
      "positive_pass": true,
      "reason": "row 0 identity fails",
      "red": true
    },
    {
      "code": "row_identity",
      "expected_codes": [
        "row_identity"
      ],
      "g6": "J??QIOwi\\k?",
      "name": "real-dag: final cofactors removed",
      "positive_pass": true,
      "reason": "row 12 identity fails",
      "red": true
    },
    {
      "code": "frame",
      "expected_codes": [
        "frame"
      ],
      "g6": "J??QIOwi\\k?",
      "name": "real-dag: invalid frame",
      "positive_pass": true,
      "reason": "frame is not an actual edge",
      "red": true
    },
    {
      "code": "last_target",
      "expected_codes": [
        "last_target"
      ],
      "g6": "J??QIOwi\\k?",
      "name": "real-dag: target coefficient perturbed",
      "positive_pass": true,
      "reason": "last row is not the required target",
      "red": true
    },
    {
      "code": "sos_identity",
      "expected_codes": [
        "sos_identity"
      ],
      "g6": "J?aPROSOj`_",
      "name": "real+sos: SOS constant +1",
      "positive_pass": true,
      "reason": "SOS identity fails",
      "red": true
    },
    {
      "code": "sos_identity",
      "expected_codes": [
        "sos_identity"
      ],
      "g6": "J?aPROSOj`_",
      "name": "real+sos: SOS weight doubled",
      "positive_pass": true,
      "reason": "SOS identity fails",
      "red": true
    },
    {
      "code": "sos_identity",
      "expected_codes": [
        "sos_identity"
      ],
      "g6": "J??QIOwi\\k?",
      "name": "real-dag+sos: SOS constant +1",
      "positive_pass": true,
      "reason": "SOS identity fails",
      "red": true
    },
    {
      "code": "sos_identity",
      "expected_codes": [
        "sos_identity"
      ],
      "g6": "J??QIOwi\\k?",
      "name": "real-dag+sos: SOS weight doubled",
      "positive_pass": true,
      "reason": "SOS identity fails",
      "red": true
    },
    {
      "code": "tree_rowspace",
      "expected_codes": [
        "tree_rowspace"
      ],
      "g6": "J???]OsBfb_",
      "name": "tree: matrix entry +1",
      "positive_pass": true,
      "reason": "regenerated constraint row space differs at root",
      "red": true
    },
    {
      "code": "tree_discriminant",
      "expected_codes": [
        "tree_discriminant"
      ],
      "g6": "J???]OsBfb_",
      "name": "tree: L3 d +2",
      "positive_pass": true,
      "reason": "L3 d^2 identity fails at root",
      "red": true
    }
  ],
  "scanned_records": 448708,
  "scope": "provided-stream",
  "seconds": 881.341,
  "seed": 20261007,
  "selected_records": 448708,
  "selected_sha256": "41731c987fade25c26b205fb02c809a2b75461ddeae852869ad61aab2804e114",
  "shard": "0/1",
  "source_hashes": {
    "independent_core.py": "898b416487e0727dbeb316761ee08093d33b705b0cfc7b3b4a30acedb973f1e5",
    "modp_identities.py": "1ddde93141b50297491c966ceab1a243f3601aa7aa324c323c34e96fff0ed202"
  },
  "status": "PASS",
  "tree_method": "regenerated rhombi and row spaces over modular quotient rings; random remainder evaluation plus coefficient equality",
  "worker_seconds": 1355.16
}