Re-Phase Vol.4.4: Local Directional Fragility — Fréchet Derivatives, Linearized Admissible Directions, and Feature-Sensitive Perturbations

This volume develops the deterministic local directional layer of the Re-Phase framework. It reformulates earlier fiber-shrinking and weak-direction intuition as linearized admissible first-order direction diagnostics. Using Fréchet derivatives of nonlinear condition and feature maps, the note studies directions that are weakly visible to local observation but strongly affect a target feature. The construction is local, deterministic, and first-order. It distinguishes necessary linearized constraints from tangent-space equality under regularity, and treats Gram and Rayleigh objects only as inner-product dependent diagnostics. Fisher-weighted local geometry, path-space continuation, guard selection, gauge-like structures, and cohomological issues are deferred to later volumes.