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| """Independent raw-witness checker for Claim 2.""" | |
| from __future__ import annotations | |
| import itertools | |
| import json | |
| from pathlib import Path | |
| import numpy as np | |
| from .claim1 import structural | |
| def check(runtime_dir: Path) -> dict[str, object]: | |
| witnesses = json.loads((runtime_dir / "claim_2_witnesses.json").read_text()) | |
| rows = json.loads((runtime_dir / "claim_2_dispersion_rows.json").read_text()) | |
| pseudo = json.loads( | |
| (runtime_dir / "claim_2_pseudometric_rows.json").read_text() | |
| ) | |
| maximum_error = 0.0 | |
| marginal_error = 0.0 | |
| for witness, recorded in zip(witnesses, rows, strict=True): | |
| dx = np.asarray(witness["dx"]) | |
| dy = np.asarray(witness["dy"]) | |
| coupling = np.asarray(witness["coupling"]) | |
| n = coupling.shape[0] | |
| # Direct four-index sum, distinct from the primary einsum expression. | |
| gw = 0.0 | |
| for i, j, k, ell in itertools.product(range(n), repeat=4): | |
| gw += ( | |
| (dx[i, k] - dy[j, ell]) ** 2 | |
| * coupling[i, j] | |
| * coupling[k, ell] | |
| ) | |
| variance = gw - structural(dx, dy, coupling) | |
| maximum_error = max( | |
| maximum_error, abs(variance - recorded["dispersion_V"]) | |
| ) | |
| marginal_error = max( | |
| marginal_error, | |
| float(np.max(np.abs(coupling.sum(axis=0) - 1 / n))), | |
| float(np.max(np.abs(coupling.sum(axis=1) - 1 / n))), | |
| ) | |
| triangle_failures = sum(row["triangle_excess"] > 1e-10 for row in pseudo) | |
| grouped: dict[tuple[float, int, int], float] = {} | |
| for row in pseudo: | |
| grouped[(row["alpha"], row["x"], row["z"])] = row["d_xz"] | |
| symmetry_failures = sum( | |
| abs(distance - grouped[(alpha, z, x)]) > 1e-10 | |
| for (alpha, x, z), distance in grouped.items() | |
| ) | |
| gates = { | |
| "all_32_raw_witnesses_recomputed": bool( | |
| len(witnesses) == len(rows) == 32 | |
| ), | |
| "independent_four_index_identity_agrees": bool(maximum_error < 1e-10), | |
| "witness_marginals_exact": bool(marginal_error < 1e-10), | |
| "all_320_triangle_rows_rechecked": bool( | |
| len(pseudo) == 320 and triangle_failures == 0 | |
| ), | |
| "recorded_symmetry_rechecked": bool(symmetry_failures == 0), | |
| } | |
| result = { | |
| "checker": "raw witness four-index enumeration and table recheck", | |
| "maximum_independent_dispersion_error": float(maximum_error), | |
| "maximum_witness_marginal_error": float(marginal_error), | |
| "triangle_failures": int(triangle_failures), | |
| "symmetry_failures": int(symmetry_failures), | |
| "gates": gates, | |
| "all_gates_pass": all(gates.values()), | |
| } | |
| (runtime_dir / "claim_2_independent_checker.json").write_text( | |
| json.dumps(result, indent=2) + "\n", encoding="utf-8" | |
| ) | |
| if not result["all_gates_pass"]: | |
| raise RuntimeError("Independent Claim 2 checker failed") | |
| return result | |