WuXing and Cl(6,6): 144 Pentads for a Unified Relational Physics

We propose a geometric and algebraic unification of particle physics and cosmology by replacing the paradigm of quantum fields on a fixed spacetime background with a relational pre-geometric substrate based on the Clifford algebra Cl (6, 6) @Clifford1878; @Hestenes1984. Integrating P. Rowlands' nilpotent formalism (emergent spin, active vacuum, native Pauli exclusion) @Rowlands2007 and J. -P. Petit's Janus bimetric model (negative masses, self-generated expansion, Dipole Repeller) @Petit2024, we demonstrate that both frameworks are orthogonal projections of a single dual invariant. The Dirac equation is derived directly from the algebraic closure, and a unified variational principle on a 72-dimensional manifold is introduced, from which all equations of motion follow. Elementary particles are defined as stable configurations of relational angles, encoded by 144 nilpotent pentads arising from a spectral partition of Cl (6, 6) into 12 regulatory leaves. Fundamental interactions are reformulated as geometric rearrangements driven by a transition operator T, eliminating virtual gauge bosons and naturally regularizing UV/IR divergences. Using Gabriele Nebe's extremal unimodular lattice ₇₂, we diagonalize its Gram matrix to obtain 72 eigenvalues that serve as spectral frequencies for the pentad network. Applying combinatorial rules based on Merkabah triplets and Bott-periodic pre-geometric bundles, we reproduce the masses of light hadrons (, K, p) with deviations <0. 05\%, and the muon, W, Z, and Higgs bosons with deviations <0. 5\%. The electron is treated as a model constant, while heavier quarkonia (J/, ) are reproduced within 5--8\%. At the cosmological scale, the cosmological constant, dark matter, and dark energy emerge as macroscopic projections of the local coupling density between cosmic and anti-cosmic sectors. The architecture is organized across scales via Bott periodicity, with the 200~MeV resonance in magnetars identified as an inter-octave transition. This self-regulating relational framework yields testable signatures—including a predicted low-energy deviation in e^+e^- cross-sections, annular negative lensing around cosmic voids, and a strict Eₑ₄ₒ B² scaling in magnetars—and paves the way for a unified physics where micro and macro scales, as well as algebra and geometry, are two facets of the same relational invariant.