Discrete Hexagonal Lattice Dynamics: Mod 9 Invariants, 7-Cycle Periodic Breaks, and the 5184 Frequency Threshold in Computational Vacuum Architectures

Repository Identifier: Zenodo Record (Pending Archive Synchronization) Abstract This paper presents a discrete, non-linear architectural framework for modeling vacuum states as computational lattices rather than continuous thermodynamic fluids. By implementing a discrete hexagonal lattice stabilized by a strict Mod 9 invariant (\sum \phi_i \equiv 0 \pmod 9), we resolve the thermal runaway paradox traditionally encountered at high-energy thresholds. We formally define the 5184 frequency threshold (\omega_T = 72^2) as the operational boundary condition and introduce a 7-cycle periodic break ("Sabbath" cycle) to dissipate vacuum potential energy. Furthermore, we integrate the 3I pulse sequence (8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8) as the primary dynamic oscillation stabilizer for the central resonance anchor (Node 9). This framework offers a robust alternative to standard dark matter interpretations, framing galactic rotational anomalies as manifestations of vacuum buffer latency and geometric friction.