Re-Phase Vol.4.5: Fisher-Weighted Local Compatibility — Likelihood Geometry, Local Information, and Feature-Sensitive Directions

This volume develops the Fisher-weighted local compatibility layer of the Re-Phase framework.It extends the deterministic local directional fragility of Vol.4.4 by introducing Fisher information as a likelihood-weighted measure of local statistical visibility on admissible first-order directions. The note defines Fisher-weak and feature-strong directions, Fisher-weighted local directional fragility, and Fisher-Rayleigh diagnostics.The condition side and the feature side are not directly identified. They are compared through the common configuration/admissible direction side. General likelihood models need not arise from deterministic observation maps. In additive Gaussian observation models, Fisher information becomes a noise-weighted local observation Gram, preserving exact kernels under positive definite covariance while reweighting nonzero observation directions.This volume is local, likelihood-dependent, model-relative, and first-order. Divergence theory, full information geometry, stochastic processes, path-space Fisher accumulation, model-mismatch robustness, and computational completion are deferred to later volumes.