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c6eaad2 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | """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
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