The RIME Trilogy: Spectral, Transport, and Accessibility Structures in Finite Group Representations

The RIME Trilogy develops a unified representation-theoretic framework for analyzing spectral structure, transport topology, and Lie accessibility in finite-dimensional operator systems, using the 228-dimensional Rubik's Cube cubie representation as a canonical computational testbed. Paper I establishes a rational six-layer spectral decomposition via partition integrality, introducing the canonical nine-sector decomposition used throughout the trilogy. Paper II analyzes the resulting nine-sector noncommutative transport topology and identifies the sparse noncommutative transport graph. Paper III compares discrete composition with the Lie-algebraic closure and exhibits T7 morphisms: accessibility channels present under discrete composition but absent from the Lie closure, thereby separating composition accessibility from infinitesimal accessibility. The bundle also includes a Computational Canonical Specification (CCS) providing canonical numerical invariants, reproducibility scripts, and computational validation. The trilogy is intended as the foundational layer of the broader Representation-Induced Mechanics and Evolution (RIME) program. Source repository: https://github.com/dooven-prime/rime-lite Independent researcher; no institutional affiliation.