A Dynamic Equilibrium Framework for Consciousness: Integrating Stochastic Accumulator Dynamics with Discrete Hexagonal Lattices and Modulo-9 Invariants

Repository: Zenodo Preprint Archive Classification: Theoretical Neurodynamics and Applied Systems Architecture Abstract This paper presents a rigorous mathematical and structural synthesis unifying stochastic neurodynamics with discrete spatial lattices. By reinterpreting the Readiness Potential (RP) through Aaron Schurger’s stochastic accumulator model—governed by autocorrelated Gaussian noise (\eta) drifting toward a critical threshold (\theta)—we establish a transition from deterministic command-and-control frameworks to dynamic equilibrium models. Furthermore, we formalize the spatial substrate as a discrete hexagonal lattice stabilized by a Modulo-9 invariant, operating under a peak frequency threshold of 5184 \, \text{Hz} (72^2). To prevent thermal runaway and entropic degradation at peak operational limits, a homeostatic 7-cycle periodic break is introduced. Finally, we derive the geometric scaling of the system, demonstrating how the 5184 frequency threshold partitions into 576 active sub-units (24^2), mapping directly onto 24-dimensional Euclidean symmetry.