feat: add 3 external solved math problems to validation (21/21)

New problems from outside the project:
- Catalan-Mihailescu: 3^2-2^3=1 only consecutive powers λ=6.18
- Fermat-Wiles: x^n+y^n=z^n no solutions n>2 λ=7.02
- Ramanujan taxicab: 1729=1^3+12^3=9^3+10^3 λ=4.85

All 21 deterministic, 21/21 signal detected

scripts/validate_known_equations.py

@@ -157,6 +157,22 @@ EQUATIONS = [
         "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",
     },
+    # ── Random solved problem from outside the project ──────────────
+    {
+        "name": "Catalan-Mihailescu: 3^2 - 2^3 = 1 is the only consecutive perfect powers",
+        "equation": "Catalan's conjecture (Mihailescu's theorem): The only solution to x^a - y^b = 1 for a,b>1,x,y>0 is 3^2 - 2^3 = 1, i.e. 9 - 8 = 1",
+        "source": "Preda Mihailescu 2002, J. Reine Angew. Math.",
+    },
+    {
+        "name": "Fermat's Last Theorem: x^n + y^n = z^n has no solutions for n>2",
+        "equation": "Fermat's Last Theorem (Wiles 1995): x^n + y^n = z^n has no positive integer solutions for n > 2. For n=3, x^3 + y^3 = z^3 has no solutions",
+        "source": "Andrew Wiles 1995, Annals of Mathematics",
+    },
+    {
+        "name": "Ramanujan's taxicab: 1729 = 1^3 + 12^3 = 9^3 + 10^3",
+        "equation": "Ramanujan's taxicab number 1729: 1729 = 1^3 + 12^3 = 9^3 + 10^3. Smallest number expressible as sum of two cubes in two different ways",
+        "source": "G.H. Hardy, Ramanujan 1918",
+    },
 ]
 
 

signatures/known_equation_validation.json

@@ -1,8 +1,8 @@
 {
   "schema": "known_equation_validation_v1",
   "deterministic": true,
-  "total": 18,
-  "signals_detected": 18,
+  "total": 21,
+  "signals_detected": 21,
   "results": [
     {
       "name": "Erdos-Renyi critical graph G(n,1/n)",
@@ -165,6 +165,33 @@
       "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
     }
   ]
 }