DERIVING A CONSERVATION HIERARCHY FROM THE GHIDAN CAPACITY LAW

This manuscript synthesizes a set of previously published preprints into a single layered framework built around the Ghidan Capacity Conservation Law, χ² + L = 1. Its purpose is not to introduce every component for the first time, but to organize the framework into a hierarchy that separates direct consequences of the capacity law from results that require additional state-space, dynamical, and composite-system assumptions. At the base level, the conservation law defines bounded throughput and load, finite saturation behavior, and a natural angular state geometry. When embedded into a two-state complex representation, it recovers state normalization and Born-style weighting within the chosen basis. With the addition of continuity, linearity, and symmetry assumptions, the same structure supports norm-preserving evolution and Schrödinger-type dynamics. Finally, when extended to composite systems, it supports a shared-capacity entanglement geometry and, with an added rotational correlation ansatz, Tsirelson-type bounds. The central claim of the manuscript is therefore not that all of these results arise from the scalar law alone, but that they form a coherent hierarchy rooted in a common informational conservation principle. Keywords: capacity conservation, informational throughput, Bloch sphere, Born rule, unitarity, entanglement geometry, Tsirelson bound