Metastability on the hypercube I: rate functions and sharp thresholds for Metropolis dynamics

Exact exponential-scale analysis of metastability for the single-bit Metropolis chain on the binary hypercube when the fitness function depends only on the Hamming weight (K=0 case). The chain projects onto a one-dimensional birth-death chain, enabling explicit computation of the rate function, critical threshold, and freezing-threshold asymptotics via series-resistance capacity theory and discrete Laplace methods. Three results are established: equilibrium delocalization under subextensive selection, sharp hitting-time asymptotics for smooth basins with an interior saddle (Regime I), and analogous results for piecewise-smooth basins with a boundary kink (Regime II). These K=0 formulas serve as the computation…