The Chrysene Formalism: Axiomatic Foundations of a Discrete Non-Commutative Topological Space

Abstract

While continuous stochastic models and H-2 expected-variance optimization have provided profound epistemological success in characterizing macroscopic thermodynamic behavior, their reliance on unbounded Euclidean manifolds introduces critical vulnerabilities when absolute structural containment is mandated. Because continuous topologies permit unbounded differential scaling, they remain inherently susceptible to orthogonal, unobservable divergence. To resolve this geometric porousness without invalidating the utility of continuous mechanics, we formalize the Chrysene Tensor Space—a discrete, non-commutative fibrated manifold constructed over a three-dimensional integer lattice. By abstracting the physical 3,6,9,12-tetrasubstituted chrysene molecule into a rigorous mathematical topology governed by strict C2h chiral symmetry, we establish exact orthogonal quantum decoupling, continuous perimeter conductivity, and deterministic spatial translation. Furthermore, we demonstrate that absolute macroscopic containment is achieved by transitioning from probabilistic expected-case bounding to a discrete H-infinity extremal boundary. The resultant topological sequence natively operates as a Geometric Goppa Code over the Galois field GF(4), embedding strict error-correcting limits into the spatial geometry. Ultimately, this formalism establishes the invariant, deterministic mathematical bedrock required to govern complex dynamical systems and secure macroscopic topologies against continuous exogenous derivations.