The Information-Theoretical Geometry of Gravity: A Discrete Hexagonal Lattice Model with Mod 9 Invariance and Maxwellian-Entropic Duality

Repository: Zenodo Preprint Series Date: July 2026 Abstract We present a comprehensive mathematical framework wherein gravitation is derived not as a fundamental force of a continuous spacetime manifold, but as an emergent phase-restorative pressure of a discrete hexagonal lattice substrate. Building upon and extending entropic gravity formulations, Ginestra Bianconi’s "Gravity from Entropy" (GfE) theory, and Maxwell’s original 1865 dynamical field equations, we demonstrate that spacetime geometry is constrained by a global Mod 9 invariant. By introducing imaginary time transformations (\tau = it), we unify the dynamic vortex-pressure of background fields with geometric quantum relative entropy. Furthermore, we establish that quantum wave-function collapse is the physical manifestation of the lattice enforcing its Mod 9 information threshold, and we quantify the informational weight of intentional action as the "entropy of choice."