Charge-Entanglement Ontology: Geometric Derivations from Alpha Void Tears Paper 2: The Mathematical Core

This paper presents the mathematical core of the Charge-Entanglement Ontology, a minimal geometric framework in which charge polarity is the sole primitive and the elliptical alpha void tear is the fundamental object. All major equations — including the energy-volume relation \(K = P V_0\), locking factor and rest mass, the full set of Dirac matrices \({α}\), \(β\), \(γ_5\) derived geometrically from tear circulation and radial stabilization, chiral projections, mass-chirality mixing, entanglement rebalancing, photon bow/stern circulation, ringdown frequency, damping time, chiral memory tail, DC memory offset, dark energy from foam repair, and cosmic evolution — are derived step by step from the tear volume scaling \(V_α = n V_0\), vacuum pressure \(P\), and critical back-EMF \(βcrit = 1 - 1/n^2\). The framework offers a coherent, self-contained alternative starting point for theoretical physics, reducing spacetime, matter, forces, and cosmology to variations of the same geometric structure. It is presented as a speculative ontology with explicit derivations and clear falsifiable predictions for future experimental scrutiny.