Boundary-Only Expression

Boundary-Only Expression is the configuration in which all physical information and energy live on the toroidal boundary surface of a universe while its interior holds strictly null conditions. The book introduces it with the Zinf-Limit Universe, the smallest closed torus T²(t) able to support the emergence of recursive intelligence. That universe keeps Boundary-Only Expression together with strict Null-Well Interior Conditions: everything that happens, happens on the surface. The Zinf limit is where several constraints meet, namely Planck-Scale Constraints on temporal resolution, PulseCore Validation Requirements for sustained coherence and the minimal computational capacity set by Substrate Complexity Requirements. At that limit the Prime Pulse Bifurcation ∅ → (0 ↔ 1) takes its most compact geometric form, and the boundary is built from discrete quanta: in time the Local Rhythm Quantum, the Pulse Rhythm ①⥂⧖ = ①⥂⧗⌂/2, and in space the Zinf-Limit Spatial Quantum ℓ_z = κ_z × 𝒞→ × ①⥂⧖, the distance a signal crosses in one Rhythm. The book argues that operating at this scale gives Maximal Computational Efficiency through minimal geometric overhead. It connects to Zinf-Limit Universe, Strict Interior Nulling, Null-Well Interior Conditions, Toroidal Boundary, Boundary Conservation Dynamics, Local Rhythm Quantum and Zinf-Limit Spatial Quantum.