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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)
170 lines
5.5 KiB
JSON
170 lines
5.5 KiB
JSON
{
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"schema": "known_equation_validation_v1",
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"deterministic": true,
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"total": 18,
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"signals_detected": 18,
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"results": [
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{
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"name": "Erdos-Renyi critical graph G(n,1/n)",
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"lambda": 3.3665,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "dd7f3a1b03e2",
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"source": "Erdos 1976, Problem 30; eridos_renyi_quimb.py",
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"deterministic": true,
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"signal_detected": true
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},
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{
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"name": "Goormaghtigh: R(2,5) = 31",
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"lambda": 5.4862,
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"shape": "CognitiveLoadField",
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"matrix_hash": "316cfbdaba17",
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"source": "GoormaghtighEnumeration.lean, BMS 2008 bounds; Grantham 2024",
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"deterministic": true,
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"signal_detected": true
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},
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{
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"name": "Goormaghtigh: R(5,3) = 31",
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"lambda": 2.0,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "d922d57b9a8e",
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"source": "GoormaghtighEnumeration.lean",
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"deterministic": true,
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"signal_detected": true
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},
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{
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"name": "Goormaghtigh: R(2,13) = 8191",
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"lambda": 1.7712,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "4c2c7d3fdee0",
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"source": "GoormaghtighEnumeration.lean",
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"deterministic": true,
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"signal_detected": true
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},
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{
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"name": "Hachimoji N=8 uniqueness",
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"lambda": 1.8965,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "db7e1d196df5",
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"source": "HachimojiN8.lean, n8_unique theorem",
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"deterministic": true,
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"signal_detected": true
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},
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{
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"name": "Sidon set Singer construction",
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"lambda": 2.0926,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "c16a124707e9",
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"source": "SidonSets.lean, Singer 1938",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 4.1355,
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"shape": "CognitiveLoadField",
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"matrix_hash": "72c35f89debe",
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"source": "YangBaxter.lean, yang_baxter_holds theorem",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 4.4366,
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"shape": "CognitiveLoadField",
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"matrix_hash": "38efac549403",
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"source": "CartanConnection.lean, C_weight definition",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 2.1786,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "1cb1a73382f7",
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"source": "FisherRigidity.lean, spectralGapIntCompare lemma",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 2.7168,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "b164c10adc53",
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"source": "AGENTS.md meta-solid finding; hard-sphere polydispersity consensus",
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"deterministic": true,
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"signal_detected": true
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},
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{
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"name": "Erdos squarefree: C(2n,n) not squarefree for n>4 (Ramar\u00e9-Granville 1996)",
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"lambda": 6.6999,
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"shape": "CognitiveLoadField",
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"matrix_hash": "673c687daba6",
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"source": "Erdos problem solved by Ramar\u00e9 and Granville 1996",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 5.3781,
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"shape": "CognitiveLoadField",
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"matrix_hash": "25c6b1d208e5",
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"source": "Erdos problem, Moser 1953",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 3.9048,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "bff8ce968835",
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"source": "Erdos-Ginzburg-Ziv theorem 1961",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 5.949,
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"shape": "CognitiveLoadField",
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"matrix_hash": "71705d83877e",
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"source": "Erdos-Ko-Rado theorem 1938",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 5.7162,
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"shape": "CognitiveLoadField",
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"matrix_hash": "44ded6b2162f",
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"source": "Terence Tao 2015, Annals of Mathematics",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 5.2336,
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"shape": "CognitiveLoadField",
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"matrix_hash": "3dd4492b3c0c",
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"source": "Jared Duker Lichtman 2022, Annals of Mathematics",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 3.32,
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"shape": "SignalShapedRouteCompiler",
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"matrix_hash": "bca3021267be",
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"source": "Ernie Croot 2000, Annals of Mathematics",
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"deterministic": true,
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"signal_detected": true
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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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"lambda": 6.3829,
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"shape": "CognitiveLoadField",
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"matrix_hash": "42c1240f8f79",
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"source": "da Silva and Hamidoune 1994",
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"deterministic": true,
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"signal_detected": true
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}
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]
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}
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