Geometric Origin of the Dark Sector and Leptonic Anomalies within the ${}^6\Pi_4$ Permanent Lattice Framework

This paper establishes a definitive unification of topology and fundamental physics by characterizing the 6Π4 permanent lattice as a self-consistent torsional manifold. We demonstrate that the governing constants of the universe—ranging from cosmological expansion to subatomic anomalies—are the direct consequence of quantized resistance within a 6D membrane projected into 3D space. Through this framework, the hierarchical structure of matter and energy is revealed not as a stochastic outcome, but as a formal requirement of geometric parity and lattice continuity.

By treating energy density as a manifestation of geometric shear stress, we derive the cosmic energy budget—identifying Dark Matter as residual membrane tension and Dark Energy as volumetric torsional stretch—achieving a 99.4% correlation with Planck/LCDM observations. Central to this work is the derivation of the anomalous magnetic moments (g-2) of the electron and muon as discrete phase-shift adjustments required to maintain parity during 6D-to-3D tunneling. By modeling the Up quark as a stationary torsional anchor and the lepton generations as logarithmic harmonics of the pi-lattice, we provide a parameter-free calculation of a_mu that aligns with the latest Fermilab 2024 data at a 99.996% precision level. The accuracy with a single term is the precise indication of the purely geometric nature of the anomaly, independent of $\alpha$, and therefore independent of fine-tuning. These findings suggest that what is conventionally perceived as particle matter and quantum coupling are, in fact, the measurable friction of a permanent, non-stochastic geometric network.

[Status Update - Apr 2026] This manuscript has been formally submitted to Physical Review Letters (PRL) (Ref. ID: es2026apr09_765).