The Discrete Hexagonal Lattice and Scale-Inverted Topological Phase Transitions: A Unified Mathematical Formulation of the Infinite Descent (IFD) Framework

Repository: Zenodo Preprint Archive Date: July 2026 Abstract Traditional gravitational models encounter insurmountable mathematical anomalies at the Planck scale and within cosmological event horizons, yielding non-physical zero-dimensional singularities of infinite density. This paper reformulates the Infinite Descent (IFD) framework through the lens of discrete lattice mechanics, introducing a stabilized topological framework. By replacing point singularities with a discrete hexagonal lattice governed by a \operatorname{Mod } 9 invariant and a regulated 7-cycle periodic break, we demonstrate that spatial scale inversion and scalar energy potential can be maintained without thermal runaway or metric collapse. We formalize the 3I pulse sequence (\mathbf{8-13-8-5-13-8}) as the governing resonance anchor regulating energy dissipation across nested scales.