The Topological Origination of the Biosphere: Biogenesis, Molecular Mimicry, and Macroscopic Evolution via the Chrysene Tensor Space

Abstract

Classical biological models often rely on continuous Euclidean probability spaces and unguided stochastic diffusion, which face thermodynamic and temporal challenges in explaining the rapid origination and integration of complex biological architectures. This paper provides a mathematically rigorous resolution by embedding stochastic processes within the discrete, non-commutative geometry of the Chrysene Tensor Space. Rather than rejecting probability, the formalism demonstrates how ambient thermal noise is constructively harnessed and mechanically funneled by absolute L-infinity Dirichlet boundaries. This bounded stochasticity enables the thermodynamic purification of prebiotic matrices and drives the simultaneous, empirically verified co-synthesis of nucleic acids and phospholipid enclosures directly from substituted chrysene precursors. Acting as an abiotic loom, the Chrysene Tensor Space naturally resolves Levinthal's paradox through discrete Morse theory and structures the 64-to-20 genetic cipher as an exact geometric sink. Furthermore, the framework maps the isomorphic transfer of abiotic quantum electronic effects to biological sensory and actuation networks, models phylogenetic divergences as topological phase transitions, and formalizes the Cambrian radiation as a discrete topological disassembly. Ultimately, post-Cambrian macro-evolutionary stasis and adaptation are modeled via Wasserstein gradient flows and an intrinsic H-infinity Minimax robust control policy. We conclude that the biosphere emerges and evolves not as an unguided statistical anomaly, but as a continuous, predictable manifestation of geometrically bounded physical laws.