{
  "scope": "Mathematical example checks only; no empirical validation or new Lean verification",
  "checks": {
    "finite_epsilon_bridge": {
      "max_limit_error": 6.931471805593503e-05,
      "tied_minima": [
        0.5,
        0.5,
        0.0
      ]
    },
    "hidden_spin_marginal": {
      "exact_error": 2.7755575615628914e-17,
      "naive_deletion_error": 0.06291146485118743
    },
    "four_way_coupling": {
      "coefficient": 1.9989338767567588e-08,
      "leading_order": 2e-08
    },
    "relative_entropy_identity": {
      "max_error": 2.220446049250313e-16
    },
    "static_response": {
      "finite_difference": -0.9886014044169221,
      "covariance_over_epsilon": -0.9886014043606334
    },
    "memory_redescription": {
      "full_x": 0.4060058497098344,
      "reduced_x": 0.4060058497098381,
      "derivative_residual": 1.049160758270773e-14,
      "memoryless_x": 1.0
    },
    "joint_consistency": {
      "passed": true
    },
    "kummer_bookkeeping": {
      "torus": 0,
      "quotient": 8,
      "resolution": 24
    }
  }
}