feat: add 8 solved Erdos problems to validation (18/18 deterministic)

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

@@ -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",
+    },
 ]
 
 

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
     }
   ]
 }