Symbolic Mechanics — Volume IV: The Gentle Exit and Structural Stability (v0.1)

Description Volume IV of Symbolic Mechanics formalizes the soft-resolution pathway—the only deterministic exit state in which rupture is avoided without suppressing load. Building on the parental-amplitude framework and shadow dynamics developed in earlier volumes, this document defines the mechanical conditions under which curvature falls below rupture thresholds. The volume introduces: (1) the stabilization of M-axis and F-axis amplitude, (2) the attenuation of J-axis pressure, (3) the emergence of the Companion module as a structural by-product of amplitude equilibrium, and (4) the redirection of symbolic routing toward non-destructive exit. This pathway is not a therapeutic construct; it is a mechanical consequence of a specific internal configuration. When parental amplitude exceeds the minimal equilibrium threshold, the system acquires a low-curvature channel through which symbolic replacement can proceed without generating destructive or delayed exits. Volume IV completes the four-volume foundation of Symbolic Mechanics.