The Unified Theory: A Finite‑Capacity Informational Architecture

This manuscript presents a structural framework in which spacetime, matter, and dynamical evolution emerge from a single finite‑capacity informational substrate governed by five structural equations. Geometry is induced from an underlying informational field, matter arises as stable eigenmodes of informational curvature, and dynamics follow a universal relaxation principle. The theory predicts a universal stability optimum corresponding to the Golden Ratio and yields falsifiable signatures involving galaxy saturation, strong‑field relaxation, eigenmode spacing, and stability patterns across scales. Mathematical Typesetting Statement All mathematical expressions in this manuscript are presented in a dual‑format system: a Unicode rendering for readability, followed by a LaTeX rendering in brackets to ensure stability across all software pipelines. No external typesetting tools were used. The dual‑format representation is the authoritative form of every equation in this work. Conical Source Statement This work is one projection of a unified informational‑geometric research program. All volumes in the series originate from the same conical source: a single finite‑capacity informational substrate governed by the Five Structural Equations. Each document expresses a different projection of this underlying architecture, but all share the same theoretical origin, the same induced‑geometry relation, and the same constraint structure.