Local Constraints Force Incompressible Paths and Metastable Slowdown in a Minimal Reversible Spin Model

This preprint studies a minimal reversible spin system in which local single-spin-flip updates force any phase-switching path to traverse all intermediate magnetization levels. The resulting path incompressibility implies a macroscopic exposure to a central barrier region whenever the free-energy density is strictly positive there. The paper formalizes this through an incompressibility index and derives an entropy-corrected exponentially small upper bound on the conductance, together with an exponentially small upper bound on the spectral gap at low temperature. The aim is not to solve metastability in realistic interacting systems, but to isolate a clean mechanism linking local update constraints, incompressible transition paths, and slow relaxation. This preprint is deposited as a timestamped mechanism paper within a broader program on path geometry and metastable slowdown.