From 8ca87c63fbc89af2f1bc82a0aaa702261e548fb3 Mon Sep 17 00:00:00 2001 From: allaun Date: Tue, 30 Jun 2026 06:49:39 -0500 Subject: [PATCH] feat: add 8 solved Erdos problems to validation (18/18 deterministic) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 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) --- scripts/validate_known_equations.py | 41 ++++++++++++ signatures/known_equation_validation.json | 76 ++++++++++++++++++++++- 2 files changed, 115 insertions(+), 2 deletions(-) diff --git a/scripts/validate_known_equations.py b/scripts/validate_known_equations.py index 962d1e43..3f29bf1b 100644 --- a/scripts/validate_known_equations.py +++ b/scripts/validate_known_equations.py @@ -116,6 +116,47 @@ EQUATIONS = [ "equation": "1/7 threshold: one complete Sidon doubling step (1 of 7 doublings 2 to 128) consumed by size spread", "source": "AGENTS.md meta-solid finding; hard-sphere polydispersity consensus", }, + # ── Solved Erdős problems ───────────────────────────────────────── + { + "name": "Erdos squarefree: C(2n,n) not squarefree for n>4 (Ramaré-Granville 1996)", + "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", + "source": "Erdos problem solved by Ramaré and Granville 1996", + }, + { + "name": "Erdos-Moser equation: 1^1 + 2^1 = 3^1 (only known solution)", + "equation": "Erdos-Moser equation: 1^k + 2^k + ... + (m-1)^k = m^k. Only known solution: m=3, k=1, giving 1 + 2 = 3", + "source": "Erdos problem, Moser 1953", + }, + { + "name": "Erdos-Ginzburg-Ziv: every 2n-1 integers have n summing to multiple of n", + "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", + "source": "Erdos-Ginzburg-Ziv theorem 1961", + }, + { + "name": "Erdos-Ko-Rado: max intersecting k-family size is C(n-1,k-1)", + "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", + "source": "Erdos-Ko-Rado theorem 1938", + }, + { + "name": "Erdos discrepancy: any +/-1 sequence has discrepancy at least C log n (Tao 2015)", + "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", + "source": "Terence Tao 2015, Annals of Mathematics", + }, + { + "name": "Erdos primitive set: sum over primes of 1/(n log n) is maximal (Lichtman 2022)", + "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", + "source": "Jared Duker Lichtman 2022, Annals of Mathematics", + }, + { + "name": "Erdos-Graham: unity as sum of Egyptian fractions (Croot 2000)", + "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", + "source": "Ernie Croot 2000, Annals of Mathematics", + }, + { + "name": "Erdos-Heilbronn: lower bound on subset sums (da Silva-Hamidoune 1994)", + "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)", + "source": "da Silva and Hamidoune 1994", + }, ] diff --git a/signatures/known_equation_validation.json b/signatures/known_equation_validation.json index 7c3a5165..66428ee2 100644 --- a/signatures/known_equation_validation.json +++ b/signatures/known_equation_validation.json @@ -1,8 +1,8 @@ { "schema": "known_equation_validation_v1", "deterministic": true, - "total": 10, - "signals_detected": 10, + "total": 18, + "signals_detected": 18, "results": [ { "name": "Erdos-Renyi critical graph G(n,1/n)", @@ -93,6 +93,78 @@ "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 } ] }