Topological System Logic (TSF): Mechanics of the Discrete Hexagonal Lattice, Mod 9 Invariants, and the 7-Cycle Stabilization Loop

Repository Archive: Zenodo Open Archive Repository, DOI: 10.5281/zenodo.TSL2026 Abstract This paper presents a deterministic, discrete alternative to the continuous spacetime frameworks and probabilistic quantum mechanics conventionally used in holographic duality and chaotic scrambling models (such as the Sachdev-Ye-Kitaev model). By replacing statistical randomness with a rigorous geometric architecture, we introduce Topological System Logic (TSL). TSL models reality as a discrete hexagonal lattice governed rigidly by a Mod 9 invariant, a 5184 (72^2) frequency threshold, and a 3I pulse sequence vector (\vec{P} = \{8, 13, 8, 5, 13, 8\}). We demonstrate that the apparent "traversable wormholes" and chaotic scrambling limits observed in modern quantum processor experiments are instead manifestations of discrete lattice saturation, stabilized by a mandatory 7-cycle periodic break ("Sabbath" protocol). Furthermore, we provide mathematical proof that eliminating the scrambling time delay (\tau_* = 0) forces an instantaneous phase transition, collapsing distributed information density into a localized mass artifact (\rho_M) at the system's central coordinate anchor.