{
  "date": "2026-10-20",
  "arithmetic": "integers_and_exact_rationals",
  "all_passed": true,
  "checks": {
    "correspondence_1999_and_alpha": {
      "states": 64,
      "fibres": 8,
      "size_each": 8,
      "pass": true
    },
    "xor_equivariance": {
      "pairs": 4096,
      "pass": true
    },
    "projective_cube": {
      "six_coordinate_points": 32,
      "seven_coordinate_points": 64,
      "L_involution": true,
      "SO7_diagonal_determinants": true,
      "pass": true
    },
    "no_three_collinear": {
      "triples": 41664,
      "pass": true
    },
    "harmonic_completion": {
      "ordered_pairs": 4032,
      "cross_ratio": -1,
      "auxiliary_points_outside_H": true,
      "pass": true
    },
    "goldenberg_lemma6_counterexample": {
      "u": "100001",
      "x": "100000",
      "u_in_ID": true,
      "xu_in_ID": false,
      "pass": true
    },
    "alpha_not_AND_congruence": {
      "equivalent": [
        "000000",
        "100100"
      ],
      "multiplier": "100000",
      "pass": true
    },
    "partial_law_counterexamples": {
      "same_fibre": [
        "000000",
        "100100"
      ],
      "domain_h1_zero_not_saturated": true,
      "T_h_xor_h1e1_not_factorable": true,
      "pass": true
    },
    "singular_spectrum_collision": {
      "states": [
        "100111",
        "010111"
      ],
      "profiles": [
        "011",
        "101"
      ],
      "singular_values": [
        1,
        1,
        0
      ],
      "a_differs": true,
      "pass": true
    },
    "controlled_composition_not_injective": {
      "policy": "mu(h)=h",
      "inputs": 64,
      "distinct_outputs": 1,
      "mask_discarded": true,
      "pass": true
    },
    "positive_markov_counterexample": {
      "P": [
        [
          "1/2",
          "1/2"
        ],
        [
          "1/2",
          "1/2"
        ]
      ],
      "distribution_after_any_positive_number_of_steps": [
        "1/2",
        "1/2"
      ],
      "not_absorption_in_optimum": true,
      "pass": true
    }
  },
  "scope": "Independent implementation of stated finite identities; not external peer review, not empirical validation",
  "global_priority": "NOT_ESTABLISHED",
  "external_validation": "NOT_RUN",
  "truth_layer_promotion": 0
}