Deterministic Quantum Logic over the Ic Manifold: C2h Orthogonal Superselection, Aharonov-Bohm Phase Gating, and the Chrysene Isomorphism Theorem

Abstract

As computational architectures approach the single-molecule limit, the reliance on continuous Euclidean spaces and probabilistic phenomenological models presents fundamental challenges in mitigating wavepacket dispersion and signal crosstalk. In a cooperative step toward next-generation quantum automata, this paper formalizes the Ic manifold: a strictly discrete, non-commutative geometric framework bijectively mapped to a three-dimensional integer lattice. We mathematically demonstrate that deterministic quantum logic can be natively executed through discrete topological step-functions and Aharonov-Bohm phase gating. Finally, we present the Chrysene Isomorphism Theorem, proving that the precise C2h point-group symmetry and bipartite topological constraints required by this manifold are uniquely and exactly fulfilled by the 3,6,9,12-tetrasubstituted chrysene core.