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5338e3e | 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 | """Independent raw-array recomputation for the Claim 5 jaw experiment."""
from __future__ import annotations
import json
import sys
from pathlib import Path
import numpy as np
from scipy.ndimage import gaussian_filter
def check(record: dict) -> dict:
failures: list[str] = []
indices = np.asarray(record["voxel_indices"], dtype=np.int64)
weights = np.asarray(record["weights"], dtype=np.float64)
scaling = np.asarray(record["scaling"], dtype=np.float64)
kernel = record["kernel"]
grid_shape = tuple(record["voxelization"]["grid_shape"])
workspace = np.zeros(grid_shape, dtype=np.float64)
def kernel_matvec(vector: np.ndarray) -> np.ndarray:
workspace.fill(0.0)
workspace[indices[:, 0], indices[:, 1], indices[:, 2]] = vector
convolved = gaussian_filter(
workspace,
sigma=float(kernel["sigma_grid_cells"]),
mode="constant",
cval=0.0,
truncate=float(kernel["truncate_sigma"]),
)
return convolved[
indices[:, 0], indices[:, 1], indices[:, 2]
]
def apply(signal: np.ndarray) -> np.ndarray:
return scaling * kernel_matvec(weights * scaling * signal)
row_values = apply(np.ones(weights.shape[0], dtype=np.float64))
row_residual = float(np.max(np.abs(row_values - 1.0)))
if row_residual > 2e-10:
failures.append("independent constant preservation")
if abs(float(weights.sum()) - 1.0) > 1e-14:
failures.append("independent mass weights")
if np.any(weights <= 0.0) or np.any(scaling <= 0.0):
failures.append("independent positive weights/scaling")
source_index = int(record["diffusion"]["source_index"])
signal = np.zeros(weights.shape[0], dtype=np.float64)
signal[source_index] = 1.0 / weights[source_index]
snapshots = {
int(item["step"]): item
for item in record["diffusion"]["snapshots"]
}
mass_errors: list[float] = []
signal_errors: list[float] = []
l2_values: list[float] = []
roughness_values: list[float] = []
maximum_step = max(snapshots)
for step in range(maximum_step + 1):
next_signal = apply(signal)
if step in snapshots:
stored = np.asarray(snapshots[step]["signal"], dtype=np.float64)
signal_errors.append(
float(np.max(np.abs(stored - signal)))
)
mass = float(np.sum(weights * signal))
mass_errors.append(abs(mass - 1.0))
centered = signal - mass
l2_values.append(float(np.sum(weights * centered**2)))
roughness_values.append(
float(np.sum(weights * signal * (signal - next_signal)))
)
if float(signal.min()) < -2e-10:
failures.append(f"independent positivity step {step}")
if step < maximum_step:
signal = next_signal
if max(signal_errors) > 2e-11:
failures.append("independent stored-signal recomputation")
if max(mass_errors) > 2e-10:
failures.append("independent mass conservation")
if any(
later > earlier * (1.0 + 2e-9) + 1e-10
for earlier, later in zip(l2_values, l2_values[1:])
):
failures.append("independent monotone L2 smoothing")
if min(roughness_values) < -2e-8:
failures.append("independent nonnegative roughness")
if any(
later > earlier * (1.0 + 2e-8) + 1e-10
for earlier, later in zip(
roughness_values, roughness_values[1:]
)
):
failures.append("independent monotone roughness")
modalities = record["cross_modalities"]
if modalities["point_cloud"]["count"] != 5_000:
failures.append("independent point modality")
gmm = modalities["covariance_aware_gmm"]
if (
gmm["count"] != 500
or gmm.get("covariance_matrices") != 500
or gmm.get("minimum_covariance_eigenvalue", 0.0) <= 0.0
):
failures.append("independent covariance-aware GMM modality")
if modalities["sparse_armadillo_voxels"]["nonempty_voxels"] < 100:
failures.append("independent voxel modality")
return {
"claim_5_contract_pass": not failures,
"verifier": "independent_raw_recomputation",
"failures": failures,
"recomputed": {
"row_residual_max": row_residual,
"maximum_mass_error": max(mass_errors),
"maximum_stored_signal_error": max(signal_errors),
"l2_values": l2_values,
"roughness_values": roughness_values,
},
}
def main() -> None:
if len(sys.argv) != 3:
raise SystemExit(
"usage: check_claim5_independent.py RAW_JSON OUTPUT_JSON"
)
record = json.loads(Path(sys.argv[1]).read_text(encoding="utf-8"))
result = check(record)
Path(sys.argv[2]).write_text(
json.dumps(result, indent=2) + "\n", encoding="utf-8"
)
print("CLAIM5_INDEPENDENT=" + json.dumps(result, sort_keys=True))
if not result["claim_5_contract_pass"]:
raise SystemExit(1)
if __name__ == "__main__":
main()
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