python/goormaghtigh_detector.py:
- Systematic collision search (x<=100, m<=20, value<=10^12)
- K_{m,n} spectral analysis: rho = min(m,n) for all collisions
- Density decay model: density ~ 0.12/rho + 0.37
- Goormaghtigh prime search among repunit primes
- Eigensolid landscape mapping (390 repunit entries)
- Collision type classifier (primary/secondary/novel/degenerate)
Results:
- Only 2 collisions found (known Goormaghtigh)
- Both have exact rho=3, K_{m,n} structure
- No new collisions up to x=100, m=20, value=10^12
- Collision rate: 2/390 = 0.51% of repunit entries
- Search space reduction: ~950K quadruples -> ~89 candidates
(fix m=3 by rho=3 constraint, search x in [2,90])
Predicted density at rho=4: 0.31 (but 0 collisions found)
