Symbolic Mechanics — Volume V: Boundary Dynamics & Displacement Mechanics (v0.1)

Volume V of Symbolic Mechanics extends the Δ→S→L→R architecture by formalizing the geometric and mechanical laws governing boundary stability, displacement attempts, and the organism’s visible reactions under boundary compression. This report introduces the concept of the stability boundary R_s, a derived system variable shaped by parental torque, Judge enforcement, shadow curvature, and organismic displacement. It demonstrates that hesitation, recoil, immobilization, and sudden discharge are not emotional or psychological states but deterministic outputs of load redistribution failures within the symbolic engine. Volume V further establishes how changes in boundary geometry emerge from internal load modulation rather than cognitive intention, providing a unified mechanical explanation for approach–avoidance cycles, blocked transformation attempts, and the internal–external tension observed during destabilization events. This volume completes the mechanical groundwork required for understanding how structural boundary expansion enables the gentle-exit pathway formalized in Volume IV.