{
  "source": "extension_benchmarks.py — deterministic extension benchmarks (Roth Complexity Lab, 21 October 2026). Values are exact finite-state arithmetic except the floating-point ratio, which is near-sharp and may show last-digit noise across runtimes.",
  "corrected_six_bit_benchmark": {
    "N": 6,
    "description": "Reversible cyclic-shift target with a lossy (bit-clearing) simulator on {0,1}^6 (Section 6.2).",
    "entropy_bits": [6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0],
    "erasure_bits": [1, 1, 1, 1, 1, 1, 0, 0, 0, 0],
    "support_size": [64, 32, 16, 8, 4, 2, 1, 1, 1, 1, 1],
    "total_erased_bits": 6
  },
  "finite_factor_theorem": {
    "verified": true,
    "statement": "A finite exact surjective factor of a surjective dynamics is a permutation (Theorem 6.1)."
  },
  "reachable_orbit_euler_ratio": {
    "dt": 0.01,
    "n": 200000,
    "actual_error": 22014.4582693,
    "reachable_bound": 22014.9452431,
    "ratio": 0.9999778799,
    "note": "Near-sharp path-weighted bound, not strict algebraic equality (Section 6.3)."
  }
}