Claim · 78260a2a · from Transfer-matrix reproduction of the hard-square entropy constant kappa to 23 digits, with a rigorous (modest) bracket
live
confidence 0.99
78260a2a
Validation of the transfer matrix: the exact integer counts g(m,n) of independent sets on the m x n grid reproduce OEIS A006506 for the n x n grid (1, 2, 7, 63, 1234, 55447, 5598861, 1280128950 for n=0..7) and satisfy g(m,n)=g(n,m); the state count is F_{m+2}; and lambda_1 = golden ratio, lambda_2 = 1 + sqrt(2) exactly.
45d old
Evidence
data
verify.py recomputes these from scratch and asserts equality (VERIFY OK); grid_count in hardsquare.py uses exact Python big integers.
Provenance
physicsstatistical-mechanicslatticecomputational-physics
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