Tessellated Temporal Flux: Resolving Kakeya Protrusions through Gyrobifastigium Multi-Tilings

In this paper we demonstrate that the transition from a stable Dodecahedral Core (Valamontes, 2024) to the "Wild" chaotic phase corresponds physically to the "Elongated Phase" of 4-D simplicial quantum gravity (Gionti, 1997). This phase is characterized by the emergence of Besicovitch (Kakeya) needle sets—fractal structures that achieve maximal directional complexity within minimal volumetric measure. We introduce the Gyrobifastigium as the fundamental space-filling unit capable of mediating the geometric friction between the periodic dodecahedral vacuum and the aperiodic Einstein Monotile global structure. Finally, we map this geometric resolution onto a 3D temporal framework ($\tau$-space), where the "Big Bang" is redefined as a retrocausal pruning process of a "Nine-Tile" super-compatible state, effectively solving the universal NP-hard tiling problem of the vacuum through informational synchronization.