Quantum Geometry of Coupled Tetrahedral Cells in Chrono-Grid Dynamics: Exact Diagonalization, Generic Zero-Energy Kernels, and Entanglement Generation

Abstract

This is the first public release of this manuscript. We present an exact numerical study of the quantum geometry of tetrahedral building blocks in Chrono-Grid Dynamics (CGD), covering both an isolated tetrahedron and a pair of tetrahedra coupled across a shared triangular face. PRINCIPAL FINDINGS: 1. A rigorous F_2 proof that single-spin-flip kinetics is impossible — all previously studied Hamiltonians are exactly diagonal. 2. The complete space of admissibility-preserving multi-edge moves (7 moves identified, minimal move = shared-face flip). 3. A structural theorem: the face-flip kinetic term is block-diagonal in the cells' private degrees of freedom, so entanglement between cells vanishes identically at all Takt steps — despite full graph connectivity. The complete source code (Python, requiring NumPy/SciPy/SymPy) is included as a supplementary ZIP file. The manuscript corrects errors in earlier unpublished drafts and supersedes all previous versions. For correspondence: nebojsharjovanovic@gmail.com