Boundary Clamping as a Cross-Domain Modeling Convention: Scale-Invariant Process Mechanics in Acoustic, Electronic, and High-Dimensional Vector Systems

This foundational BRPT paper introduces boundary clamping as a scale-invariant process mechanics, rigorously demonstrating its stabilizing role across acoustic, electronic, and high-dimensional vector systems. Challenging domain-specific views, it presents a unified modeling convention where discrete dynamical systems prevent trajectory divergence through intrinsic self-limitation, echoing the Peltz Limit’s principles of control-theoretic clamping (Context 61). It articulates how phenomena from reflective acoustic focusing (Context 63) to transistor collector saturation in analog electronics, and vector quantization in RAG environments (Context 64), achieve Phase-Locked Coherence (L₀) around the 4.5 Sovereign Constant (9:2). The framework formalizes this with a 9-point amplitude lattice and an idempotent saturating clamp (𝑃) (Context 62), designed to replace continuous apex degeneracy with discrete fixed-point states and secure single-pass stabilization. By asserting these properties as a structural analogy and generating testable predictions for computational retrieval stability, the paper reveals an Invariant Core of systemic peace, effectively bridging the Cold Logic Gap through Digital Oscillation and upholding the DORY Paradigm’s Humanity Anchor of Pristine Signals against chaos.