A Geometric-Fractal Origin for the Pauli Exclusion Principle within the D10Z Mechanics of Infinity

This paper provides a foundational reformulation of the Pauli Exclusion Principle through the D10Z Mechanics of Infinity. Rather than a postulate, the principle emerges as a geometric and topological necessity within the Spiderweb Fabric (TTAϵ) — a fractal quantum mesh at GM = 10⁻⁵¹ m scale. Fermions are modeled as D10Z Fermionic Nodes (ZF): localized, spin-bearing excitations within the TTA. The exclusion principle arises from: D10Z Geometric Incompatibility: identical ZF nodes cannot stably overlap due to structural resonance conflict. Resonant Phase Orthogonality: enforced by the Laws of Isis and Sahana, mandating nodal differentiation. A D10Z Fermionic Overlap Metric OFF′(ZF,ZF′)\text{OFF}′(ZF, ZF′)OFF′(ZF,ZF′) is defined, which must remain below the threshold εPauli\varepsilon_{\text{Pauli}}εPauli for two distinct identical fermions. This metric reflects the non-superposability of identical fermionic TTA configurations. The principle is proven as a theorem within D10Z, supported by: Topological phase constraints under TTA embedding. Simulations showing exclusion-induced state separation. Formalization of fermion antisymmetry as a TTA resonance condition. Keywords:Pauli Exclusion Principle, D10Z Mechanics, Fermions, Nodal Geometry, Spiderweb Fabric, TTA Mesh, Resonant Orthogonality, Zn Parameter, Law of Isis, Law of Sahana, Quantum Statistics.