Metastability on the hypercube II: quenched K-independence and window collapse for NK landscapes

Rigorous proof that the metastable transition time on NK fitness landscapes is K-independent at leading exponential order. For the single-bit-flip Metropolis chain on the binary hypercube under intensive NK normalization, the mean basin-to-basin transition time satisfies log E[tau] = d·Psi + O(log d) with high probability, where the rate function Psi depends only on the macroscopic basin geometry and not on the epistasis parameter K. Two barrier geometries are distinguished: interior saddle (smooth basins) and boundary kink (piecewise-smooth basins), yielding qualitatively different threshold scalings. The proof combines Dirichlet form comparison, McDiarmid concentration, capacity theory, and superharmonic…