Spaces:
Running
Running
| """Independent numerical checker using the vectorized quadratic form.""" | |
| from __future__ import annotations | |
| import json | |
| from pathlib import Path | |
| import numpy as np | |
| from .claim1 import TOLERANCE, linear_map | |
| def check(runtime_dir: Path) -> dict[str, object]: | |
| rows = json.loads((runtime_dir / "claim_1_rows.json").read_text()) | |
| required = { | |
| "support", | |
| "alpha", | |
| "jensen_gap", | |
| "minimum_hessian_eigenvalue", | |
| "maximum_marginal_error", | |
| "monotonicity_failures", | |
| } | |
| schema_pass = all(required <= set(row) for row in rows) | |
| # This checker does not call the primary objective implementation. It | |
| # independently rebuilds a deterministic Kronecker map and verifies that | |
| # v^T A^T A v is nonnegative for unrelated random directions. | |
| rng = np.random.default_rng(134) | |
| quadratic_failures = 0 | |
| for support in (3, 5, 8, 13): | |
| dx = rng.random((support, support)) | |
| dy = rng.random((support, support)) | |
| dx = 0.5 * (dx + dx.T) | |
| dy = 0.5 * (dy + dy.T) | |
| np.fill_diagonal(dx, 0) | |
| np.fill_diagonal(dy, 0) | |
| operator = linear_map(dx, dy) | |
| for _ in range(12): | |
| direction = rng.normal(size=support * support) | |
| value = float(direction @ (operator.T @ operator) @ direction) | |
| quadratic_failures += int(value < -TOLERANCE) | |
| gates = { | |
| "raw_schema_valid": schema_pass and len(rows) == 60, | |
| "recorded_jensen_nonnegative": min(row["jensen_gap"] for row in rows) | |
| >= -TOLERANCE, | |
| "recorded_hessians_psd": min( | |
| row["minimum_hessian_eigenvalue"] for row in rows | |
| ) | |
| >= -1e-8, | |
| "independent_quadratic_forms_nonnegative": quadratic_failures == 0, | |
| "recorded_marginals_exact": max( | |
| row["maximum_marginal_error"] for row in rows | |
| ) | |
| < TOLERANCE, | |
| "recorded_fw_monotone": sum( | |
| row["monotonicity_failures"] for row in rows | |
| ) | |
| == 0, | |
| } | |
| result = { | |
| "checker": "independent vectorized A.T@A quadratic-form audit", | |
| "independent_seed": 134, | |
| "quadratic_forms_checked": 48, | |
| "quadratic_failures": quadratic_failures, | |
| "gates": gates, | |
| "all_gates_pass": all(gates.values()), | |
| } | |
| (runtime_dir / "claim_1_independent_checker.json").write_text( | |
| json.dumps(result, indent=2) + "\n", encoding="utf-8" | |
| ) | |
| if not result["all_gates_pass"]: | |
| raise RuntimeError("Independent Claim 1 checker failed") | |
| return result | |