Spaces:
Running
Running
File size: 2,935 Bytes
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 75 76 77 78 | """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
|