FROM CORRELATIONS TO CURVATURE: Projective Correlation Theory

A pregeometric framework in which correlations and global compatibility constraints are taken as primitive, while spacetime geometry, matter content, and quantum behaviour arise only as emergent, projected observables. The core construction specifies a constraint manifold equipped with a correlation kernel and a family of projection maps into an effective manifold, from which metric structure, causal cones, and relativistic propagation can be reconstructed from induced two-point correlators. Quantum statistics are treated measure-theoretically, with outcome weights determined by the compatible preimage structure of the projection, providing a route to Born-type probabilities. The program is designed to reproduce established low-energy limits when calibrated, while enabling falsifiable deviation claims and direct numerical exploration on discrete realizations.