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beea5e8 | 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 | """Executable verifier for the five-diagram NTK-mean recursion claim."""
import hashlib
import json
from reproduction.diagram_rules import enumerate_diagrams
EXPECTED_IDS = {
"delta_omega:K1",
"delta_omega:V",
"sigma_prime_pair:D",
"sigma_prime_pair:F",
"sigma_prime_pair:Theta1",
}
EXPECTED_COEFFICIENTS = {
"delta_omega:K1": "1/2",
"delta_omega:V": "1/8",
"sigma_prime_pair:D": "1/2",
"sigma_prime_pair:F": "1",
"sigma_prime_pair:Theta1": "1",
}
def verify(drop_vertex: str | None = None) -> dict:
diagrams = enumerate_diagrams(drop_vertex=drop_vertex)
ids = {diagram["id"] for diagram in diagrams}
coefficients = {
diagram["id"]: diagram["correction_vertex"]["coefficient"]
for diagram in diagrams
}
checks = {
"exactly_five_diagrams": len(diagrams) == 5,
"complete_unique_topologies": ids == EXPECTED_IDS,
"paper_coefficients_match": coefficients == EXPECTED_COEFFICIENTS,
"two_quadratic_vertices": sum(
name.endswith(("Theta1", "K1")) for name in ids
) == 2,
"three_quartic_vertices": sum(
name.endswith(("V", "D", "F")) for name in ids
) == 3,
}
certificate = {
"claim": "Section 5.1 order-1/n NTK-mean recursion has exactly five diagrams",
"source": {
"arxiv": "2508.11522v4",
"html_anchor": "S5.SS1",
"equation_anchor": "S5.E12",
"source_sha256": "5237b9fec2f128b23266771acbc8e44837619d5309cd32840ce537071b64c47f",
},
"diagrams": diagrams,
"checks": checks,
"passed": all(checks.values()),
}
canonical = json.dumps(certificate, sort_keys=True, separators=(",", ":"))
certificate["certificate_sha256"] = hashlib.sha256(canonical.encode()).hexdigest()
return certificate
def main() -> int:
result = verify()
print(json.dumps(result, indent=2, sort_keys=True))
return 0 if result["passed"] else 1
if __name__ == "__main__":
raise SystemExit(main())
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