Inflativity: A Geometric Unified Field Theory in GA ℝ₄,₀,₁

The unification of General Relativity (GR) and Quantum Mechanics (QM) remains a central challenge in modern physics. Inflativity introduces a deterministic, geometric unified field theory formulated in the geometric algebra ℝ₄,₀,₁. Time is redefined as an emergent scalar arising from accumulated displacement along a fourth spatial dimension (𝐞₄), and all physical laws follow from the conservation of four-dimensional spatial expansion, |𝐔|² = C₄². From this invariant, the Lorentz transformation and a gravitational field equation equivalent to the Schwarzschild solution are derived without invoking spacetime curvature. The statistical Born rule arises naturally from the projection of a 4D multivector state into a 3D observational subspace. The resulting Inflativity Field Equation (IFE) reproduces gravitational and galactic-scale dynamics and provides a falsifiable, quantitative alternative to the dark-matter hypothesis.