Dual-Channel Information Topology in the Chrysene Formalism: Noncommutative Transport, Latent-State Dynamics, and a Falsifiable Cognitive Interpretation

Abstract

We develop a dual-channel information topology as a model-relative extension of the twelve-axiom Chrysene Formalism. The inherited molecular structure supplies inequivalent C3--C9 and C12--C6 directional data, but does not by itself imply Euclidean orthogonality, electronic isolation, transfer anisotropy, or cognitive function. We therefore separate four levels: the protected Chrysene foundation; definitional channel mathematics; realization-specific transport and hidden-state hypotheses; and formal cognitive/neuromorphic interpretation. The mathematical extension introduces channel-saturation topologies, a four-state Boolean channel lattice distinct from the inherited four-state cipher, a direct-sum transport model with quantitative residual leakage, and a three-sector crosspoint space comprising a C3--C9 control pathway, a persistent internal-state sector, and a C12--C6 readout pathway. Eliminating the hidden block yields an exact memory-kernel representation of the accessible dynamics; a finite-time linear observation space characterizes state discrimination, while a separately defined generated dynamical algebra records multiplicative growth. Oriented reachability yields a complete Heyting algebra and non-Boolean intuitionistic semantics. A corrected four-terminal bipartite/Hückel core model further shows that both intended terminal pairs are transmission-permitted but electronically inequivalent, with selective cross-terminal interference zeros on one delocalized chrysene π substrate. We then prove a finite neuromorphic consistency result in which unequal response scales, persistent hidden state, bounded nonzero direct cross-talk, state-mediated influence, rapid automatic processing, and later reportable accessibility can coexist without assigning consciousness to a molecular channel. Physical realization, transport-time ordering, and cognitive adequacy remain independently testable claims.