Barrier Equivalence and Metastable Walls for Monster Problems (Version 4.3.1, Pressure Maps & Coupling Lemmas)

Version 4.3.1 advances the structural program initiated in Versions 4.1–4.3 by introducing qualitative pressure-coupling lemmas that formalize how height-lowering pressure propagates across equivalence classes of Monster Problems inhabiting the same metastable wall. Previous versions established the catalogue of barrier-equivalence candidates and recorded worked examples as conceptual “pressure maps.” The present version consolidates this framing by isolating three qualitative lemmas—stability, closure under composition, and equivalence via persistent bidirectional coupling—providing a structural mechanism by which height reductions in one Monster are expected to induce bounded reductions in others. These lemmas mark the transition from descriptive architecture to formal structural behavior. Quantitative interlocks and toy-model reductions are deferred to Version 5.0 and beyond.