Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology

We present Hypatian Physics, a Lean4-verified framework that unifies quantum gravity, particle physics, and cosmology via a recursive algebraic-geometric formulation. Our approach formalizes fundamental structures such as recursive Jordan algebras, p-adic metric spaces, and recursive renormalization group flows. The theory yields empirically testable predictions, including gravitational wave echoes, non-zero fermion masses via Yukawa couplings, and fractal spacetime geometries consistent with cosmological observations.