Deterministic Projection Theory: A Geometric Framework for Quantum-Classical Emergence

We present the Deterministic Projection Theory (TPD), a geometric framework in which the observed four-dimensional spacetime (N,gμν) arises as the projection of a higher-dimensional fundamental manifold (M,gAB), with dim M=D≥5. Classical determinism emerges from the projection map P when detG(dP)→1, where detG(dP) is the Gram determinant of the Jacobian, while quantum indeterminacy corresponds to the regime detG(dP)→0. The central dynamical object is the novel tensor Q~μν, which modifies Einstein's field equations and yields automatic on-shell conservation. The theory unifies the radion, the projective axion, and the dilaton, providing a geometric explanation for inflation, baryon asymmetry (η∼10−9), and a resolution for black-hole singularities. We identify six falsifiable predictions, including a dynamic dark energy equation of state w(z)=−1 testable with upcoming DESI DR2 data.