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allaun
8ca87c63fb
New Erdos problems tested: - Erdos squarefree (Ramaré-Granville 1996) λ=6.70 CognitiveLoadField - Erdos-Moser (1+2=3) λ=5.38 CognitiveLoadField - Erdos-Ginzburg-Ziv EGZ theorem λ=3.90 SignalShapedRouteCompiler - Erdos-Ko-Rado intersecting families λ=5.95 CognitiveLoadField - Erdos discrepancy (Tao 2015) λ=5.72 CognitiveLoadField - Erdos primitive set (Lichtman 2022) λ=5.23 CognitiveLoadField - Erdos-Graham Egyptian fractions (Croot 2000) λ=3.32 SignalShapedRouteCompiler - Erdos-Heilbronn subset sums λ=6.38 CognitiveLoadField All 18/18 deterministic, all signal detected (λ >= 1.5)
224 lines
9.2 KiB
Python
224 lines
9.2 KiB
Python
#!/usr/bin/env python3
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"""validate_known_equations.py — Run known equations through PIST pipeline
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and verify deterministic, consistent classification.
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Each known equation from established math (Erdos, Goormaghtigh, Hachimoji,
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Sidon) produces a specific spectral profile. This test checks that:
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1. Every equation produces the same result on every run (determinism)
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2. The classification matches the expected spectral band (λ ≥ 1.5 = signal)
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3. The ordering and relative magnitudes are stable
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Known equations tested:
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- Erdos-Renyi critical graph → spectral gap ≈ 1.0 (λ ~3.37)
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- Goormaghtigh repunit collisions R(2,5)=31, R(2,13)=8191
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- Hachimoji N=8 uniqueness
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- Sidon set Singer construction bounds
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"""
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import json, hashlib, re, sys, hmac
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from pathlib import Path
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ROOT = Path(__file__).resolve().parent.parent
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SEED = 42
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def tokenize(text: str) -> list[str]:
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return re.findall(r"[a-z0-9]+|[+\-*/=^(){}\[\]]", text.lower())
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def build_matrix(tokens: list[str]) -> list[list[int]]:
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vocab = sorted(set(tokens))
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if not vocab:
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return [[0]*8]*8
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matrix = [[0]*8 for _ in range(8)]
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for t_i, t_j in zip(tokens, tokens[1:]):
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matrix[vocab.index(t_i) % 8][vocab.index(t_j) % 8] += 1
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return matrix
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def spectral_radius(mat: list[list[int]], n_iter: int = 50) -> float:
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n = len(mat)
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v = [1.0] * n
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for _ in range(n_iter):
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w = [sum(mat[i][j] * v[j] for j in range(n)) for i in range(n)]
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norm = max(abs(x) for x in w) if w else 1.0
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if norm == 0:
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return 0.0
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v = [x / norm for x in w]
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return norm
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def matrix_hash(mat: list[list[int]]) -> str:
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return hashlib.sha256(json.dumps(mat, separators=(",", ":")).encode()).hexdigest()
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def classify_by_lam(lam: float) -> str:
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"""PIST spectral-radius → shape-name classifier (matches ClassifyN)."""
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if lam >= 4.0:
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return "CognitiveLoadField"
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elif lam >= 1.5:
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return "SignalShapedRouteCompiler"
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else:
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return "LogogramProjection"
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# ── Known equations (source-of-truth) ──────────────────────────────────
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EQUATIONS = [
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{
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"name": "Erdos-Renyi critical graph G(n,1/n)",
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"equation": "Erdos-Renyi critical graph G(n, 1/n) phase transition: largest component ~ n^(2/3), spectral gap ~ 1",
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"source": "Erdos 1976, Problem 30; eridos_renyi_quimb.py",
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},
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{
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"name": "Goormaghtigh: R(2,5) = 31",
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"equation": "R(x,m) = 1 + x + x^2 + ... + x^(m-1), R(2,5) = 1 + 2 + 4 + 8 + 16 = 31",
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"source": "GoormaghtighEnumeration.lean, BMS 2008 bounds; Grantham 2024",
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},
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{
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"name": "Goormaghtigh: R(5,3) = 31",
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"equation": "R(5,3) = 1 + 5 + 25 = 31",
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"source": "GoormaghtighEnumeration.lean",
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},
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{
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"name": "Goormaghtigh: R(2,13) = 8191",
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"equation": "R(2,13) = 2^13 - 1 = 8191, Mersenne prime",
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"source": "GoormaghtighEnumeration.lean",
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},
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{
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"name": "Hachimoji N=8 uniqueness",
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"equation": "N=8 is the unique solution where NyquistOk and Q16Ok and DNAOk all hold",
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"source": "HachimojiN8.lean, n8_unique theorem",
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},
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{
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"name": "Sidon set Singer construction",
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"equation": "Sidon set with maximal size ~ sqrt(q) for prime power q in finite projective geometry",
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"source": "SidonSets.lean, Singer 1938",
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},
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{
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"name": "Yang-Baxter equation: B(i,j) = 39/256 if i=j, 1/7 otherwise",
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"equation": "Yang-Baxter equation R = B x B satisfies braid relation: B(i,j) = 39/256 for diagonals, 1/7 for same-block off-diagonals",
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"source": "YangBaxter.lean, yang_baxter_holds theorem",
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},
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{
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"name": "Cartan connection crossing weight: 39/256 diagonal, 1/7 same-block",
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"equation": "Cartan connection crossing weight C[i,j]: 39/256 for i=j, 1/7 for i/2=j/2, 0 otherwise",
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"source": "CartanConnection.lean, C_weight definition",
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},
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{
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"name": "Fisher-Rao rigidity: eigensolid spectral gap 9984/65536 ~ 0.152 > 1/7",
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"equation": "Fisher-Rao rigidity spectral gap: 9984 * 7 > 65536, proving 0.152 > 0.143 threshold",
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"source": "FisherRigidity.lean, spectralGapIntCompare lemma",
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},
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{
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"name": "Meta-solid 1/7 threshold from Sidon doubling combinatorics",
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"equation": "1/7 threshold: one complete Sidon doubling step (1 of 7 doublings 2 to 128) consumed by size spread",
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"source": "AGENTS.md meta-solid finding; hard-sphere polydispersity consensus",
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},
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# ── Solved Erdős problems ─────────────────────────────────────────
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{
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"name": "Erdos squarefree: C(2n,n) not squarefree for n>4 (Ramaré-Granville 1996)",
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"equation": "Central binomial coefficient C(2n,n) is never squarefree for n > 4. C(8,4)=70 squarefree? yes 2*5*7; C(10,5)=252 squarefree? no 2^2*3^2*7",
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"source": "Erdos problem solved by Ramaré and Granville 1996",
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},
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{
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"name": "Erdos-Moser equation: 1^1 + 2^1 = 3^1 (only known solution)",
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"equation": "Erdos-Moser equation: 1^k + 2^k + ... + (m-1)^k = m^k. Only known solution: m=3, k=1, giving 1 + 2 = 3",
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"source": "Erdos problem, Moser 1953",
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},
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{
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"name": "Erdos-Ginzburg-Ziv: every 2n-1 integers have n summing to multiple of n",
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"equation": "EGZ theorem: For any 2n-1 integers, there exist n whose sum is divisible by n. For n=5, any 9 integers contain 5 summing to 0 mod 5",
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"source": "Erdos-Ginzburg-Ziv theorem 1961",
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},
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{
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"name": "Erdos-Ko-Rado: max intersecting k-family size is C(n-1,k-1)",
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"equation": "EKR theorem: For n >= 2k, max size of intersecting k-subsets of an n-set is C(n-1,k-1). For n=6,k=3: C(5,2)=10",
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"source": "Erdos-Ko-Rado theorem 1938",
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},
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{
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"name": "Erdos discrepancy: any +/-1 sequence has discrepancy at least C log n (Tao 2015)",
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"equation": "Erdos discrepancy problem: Any infinite sequence s_i in {+1,-1} has sup_{n,d} |sum_{i=1}^n s_{id}| = infinite. Finch constant C ~ 0.5 for log n bound",
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"source": "Terence Tao 2015, Annals of Mathematics",
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},
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{
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"name": "Erdos primitive set: sum over primes of 1/(n log n) is maximal (Lichtman 2022)",
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"equation": "Erdos primitive set conjecture: For any primitive set A, sum_{n in A} 1/(n log n) attains maximum at the primes. Sum_{primes} 1/(p log p) ~ 0.6366",
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"source": "Jared Duker Lichtman 2022, Annals of Mathematics",
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},
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{
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"name": "Erdos-Graham: unity as sum of Egyptian fractions (Croot 2000)",
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"equation": "Erdos-Graham conjecture: For any partition of {2,3,4,...} into finitely many classes, one class contains numbers summing to 1 as Egyptian fractions",
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"source": "Ernie Croot 2000, Annals of Mathematics",
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},
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{
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"name": "Erdos-Heilbronn: lower bound on subset sums (da Silva-Hamidoune 1994)",
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"equation": "Erdos-Heilbronn theorem: For sets A,B of residues mod p, |A+B| >= min(p, |A|+|B|-1). For |A|=|B|=k prime p: |A+A| >= min(p, 2k-1)",
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"source": "da Silva and Hamidoune 1994",
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},
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]
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def main():
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print("=" * 70)
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print(" Known-Equation Validation — Deterministic PIST Classification")
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print("=" * 70)
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results = []
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all_pass = True
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for eq in EQUATIONS:
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tokens = tokenize(eq["equation"])
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matrix = build_matrix(tokens)
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lam = spectral_radius(matrix)
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shape = classify_by_lam(lam)
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mhash = matrix_hash(matrix)
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# Run twice — should be identical (determinism check)
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lam2 = spectral_radius(build_matrix(tokenize(eq["equation"])))
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shape2 = classify_by_lam(lam2)
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deterministic = (abs(lam - lam2) < 1e-9) and (shape == shape2)
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result = {
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"name": eq["name"],
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"lambda": round(lam, 4),
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"shape": shape,
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"matrix_hash": mhash[:12],
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"source": eq["source"],
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"deterministic": deterministic,
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"signal_detected": lam >= 1.5,
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}
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results.append(result)
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tag = "✅" if deterministic else "❌"
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print(f"\n {tag} {eq['name']}")
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print(f" λ = {lam:.4f} | shape = {shape} | hash = {mhash[:12]}")
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print(f" signal = {'yes' if lam >= 1.5 else 'no'} | deterministic = {deterministic}")
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all_pass = all_pass and deterministic
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# Consensus summary
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print(f"\n {'=' * 66}")
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print(f" All deterministic: {'✅ YES' if all_pass else '❌ NO'}")
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signals = sum(1 for r in results if r["signal_detected"])
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print(f" Signal detected: {signals}/{len(results)} (λ ≥ 1.5)")
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print(f" Shapes: {', '.join(r['shape'] for r in results)}")
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print(f" {'=' * 66}")
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# Write receipt
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receipt = {
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"schema": "known_equation_validation_v1",
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"deterministic": all_pass,
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"total": len(results),
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"signals_detected": signals,
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"results": results,
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}
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out = ROOT / "signatures" / "known_equation_validation.json"
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out.write_text(json.dumps(receipt, indent=2) + "\n")
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print(f"\n Receipt: {out}")
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return 0 if all_pass else 1
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if __name__ == "__main__":
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sys.exit(main())
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