{
  "schema": "known_equation_validation_v1",
  "deterministic": true,
  "total": 21,
  "signals_detected": 21,
  "results": [
    {
      "name": "Erdos-Renyi critical graph G(n,1/n)",
      "lambda": 3.3665,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "dd7f3a1b03e2",
      "source": "Erdos 1976, Problem 30; eridos_renyi_quimb.py",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Goormaghtigh: R(2,5) = 31",
      "lambda": 5.4862,
      "shape": "CognitiveLoadField",
      "matrix_hash": "316cfbdaba17",
      "source": "GoormaghtighEnumeration.lean, BMS 2008 bounds; Grantham 2024",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Goormaghtigh: R(5,3) = 31",
      "lambda": 2.0,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "d922d57b9a8e",
      "source": "GoormaghtighEnumeration.lean",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Goormaghtigh: R(2,13) = 8191",
      "lambda": 1.7712,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "4c2c7d3fdee0",
      "source": "GoormaghtighEnumeration.lean",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Hachimoji N=8 uniqueness",
      "lambda": 1.8965,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "db7e1d196df5",
      "source": "HachimojiN8.lean, n8_unique theorem",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Sidon set Singer construction",
      "lambda": 2.0926,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "c16a124707e9",
      "source": "SidonSets.lean, Singer 1938",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Yang-Baxter equation: B(i,j) = 39/256 if i=j, 1/7 otherwise",
      "lambda": 4.1355,
      "shape": "CognitiveLoadField",
      "matrix_hash": "72c35f89debe",
      "source": "YangBaxter.lean, yang_baxter_holds theorem",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Cartan connection crossing weight: 39/256 diagonal, 1/7 same-block",
      "lambda": 4.4366,
      "shape": "CognitiveLoadField",
      "matrix_hash": "38efac549403",
      "source": "CartanConnection.lean, C_weight definition",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Fisher-Rao rigidity: eigensolid spectral gap 9984/65536 ~ 0.152 > 1/7",
      "lambda": 2.1786,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "1cb1a73382f7",
      "source": "FisherRigidity.lean, spectralGapIntCompare lemma",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Meta-solid 1/7 threshold from Sidon doubling combinatorics",
      "lambda": 2.7168,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "b164c10adc53",
      "source": "AGENTS.md meta-solid finding; hard-sphere polydispersity consensus",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos squarefree: C(2n,n) not squarefree for n>4 (Ramar\u00e9-Granville 1996)",
      "lambda": 6.6999,
      "shape": "CognitiveLoadField",
      "matrix_hash": "673c687daba6",
      "source": "Erdos problem solved by Ramar\u00e9 and Granville 1996",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos-Moser equation: 1^1 + 2^1 = 3^1 (only known solution)",
      "lambda": 5.3781,
      "shape": "CognitiveLoadField",
      "matrix_hash": "25c6b1d208e5",
      "source": "Erdos problem, Moser 1953",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos-Ginzburg-Ziv: every 2n-1 integers have n summing to multiple of n",
      "lambda": 3.9048,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "bff8ce968835",
      "source": "Erdos-Ginzburg-Ziv theorem 1961",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos-Ko-Rado: max intersecting k-family size is C(n-1,k-1)",
      "lambda": 5.949,
      "shape": "CognitiveLoadField",
      "matrix_hash": "71705d83877e",
      "source": "Erdos-Ko-Rado theorem 1938",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos discrepancy: any +/-1 sequence has discrepancy at least C log n (Tao 2015)",
      "lambda": 5.7162,
      "shape": "CognitiveLoadField",
      "matrix_hash": "44ded6b2162f",
      "source": "Terence Tao 2015, Annals of Mathematics",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos primitive set: sum over primes of 1/(n log n) is maximal (Lichtman 2022)",
      "lambda": 5.2336,
      "shape": "CognitiveLoadField",
      "matrix_hash": "3dd4492b3c0c",
      "source": "Jared Duker Lichtman 2022, Annals of Mathematics",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos-Graham: unity as sum of Egyptian fractions (Croot 2000)",
      "lambda": 3.32,
      "shape": "SignalShapedRouteCompiler",
      "matrix_hash": "bca3021267be",
      "source": "Ernie Croot 2000, Annals of Mathematics",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Erdos-Heilbronn: lower bound on subset sums (da Silva-Hamidoune 1994)",
      "lambda": 6.3829,
      "shape": "CognitiveLoadField",
      "matrix_hash": "42c1240f8f79",
      "source": "da Silva and Hamidoune 1994",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Catalan-Mihailescu: 3^2 - 2^3 = 1 is the only consecutive perfect powers",
      "lambda": 6.1796,
      "shape": "CognitiveLoadField",
      "matrix_hash": "d2c5bcb7d6d9",
      "source": "Preda Mihailescu 2002, J. Reine Angew. Math.",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Fermat's Last Theorem: x^n + y^n = z^n has no solutions for n>2",
      "lambda": 7.0152,
      "shape": "CognitiveLoadField",
      "matrix_hash": "423474b81ebd",
      "source": "Andrew Wiles 1995, Annals of Mathematics",
      "deterministic": true,
      "signal_detected": true
    },
    {
      "name": "Ramanujan's taxicab: 1729 = 1^3 + 12^3 = 9^3 + 10^3",
      "lambda": 4.8493,
      "shape": "CognitiveLoadField",
      "matrix_hash": "9c47f0aa47eb",
      "source": "G.H. Hardy, Ramanujan 1918",
      "deterministic": true,
      "signal_detected": true
    }
  ]
}
