Dynamical Evolution of the Ic Manifold: Thermodynamically Driven Recursive Cascades and Bijective Information Transfer

Abstract

While the foundational axiomatization of the Chrysene Tensor Space Ic successfully established the deterministic H-infinity extremal boundary to rigorously contain macroscopic topologies, the temporal and kinematic evolution of this discrete non-commutative manifold requires a formal dynamical extension. In a cooperative departure from continuous stochastic probability spaces and H2 expected-variance models, this paper maps the structural evolution of the Ic manifold bijectively to the architecture of a Deterministic Finite-State Machine (DFSM). We formalize the exact thermodynamic mapping connecting dimensionless geometric displacement to absolute energy scalars strictly bounded by ambient thermal noise. Through the systematic deployment of bounded non-commutative operators—specifically, Topological Scission, Intramolecular Closure, Cross-Layer Insertion, and Recursive Ring Closure —we mathematically prove that macroscopic topological phase transitions evaluate exclusively as thermodynamically driven recursive cascades. Crucially, by integrating the Landauer limit of computation directly into the tensor space, we resolve the thermodynamic duality of the manifold: demonstrating that the structural shedding of physical lattice states guarantees absolute physical irreversibility while simultaneously enforcing a mathematically lossless, bijective mapping of the encoded informational core. Ultimately, this framework establishes that the invariant C2h chiral symmetries of the lattice dictate an exact, deterministic transfer of Base-4 logic, seamlessly bridging pure operator algebras with the physical reality of supramolecular computation.