Inflativity: A Geometric Unified Field Theory

The unification of general relativity and quantum mechanics remains a central challenge of modern physics. Inflativity introduces a deterministic geometric unified field theory formulated within a four-dimensional Euclidean spatial manifold extended by a null direction. Time is defined as an emergent scalar proportional to accumulated displacement along the fourth spatial dimension. All relativistic and quantum phenomena follow from the conservation of total four-dimensional expansion, expressed as |U|² = C₄², where U is the four-dimensional expansion vector and C₄ is a universal constant. From this invariant, the Lorentz transformation and a gravitational field equation equivalent to the Schwarzschild solution are derived without invoking spacetime curvature. The Born-rule probability relation emerges geometrically from the deterministic projection of a four-dimensional state into the observable three-dimensional domain. The resulting Inflativity Field Equation unifies relativistic dynamics, galactic rotation behaviour, and quantum measurement within a single predictive framework that yields distinct observational tests involving galaxy kinematics, photon arrival modulations, and finite black-hole interiors.