PROJECTIVE CORRELATION THEORY (PCT): Pregeometric Correlations and Projection Constraints in the Emergence of Spacetime, Matter, and Quantum Statistics

Projective Correlation Theory (PCT) is presented as a kinematic pregeometricframework in which a two-point correlator on a primitive measurable space candefine metric and causal structures only where explicit admissibility assumptionshold. Starting from a positive semi-definite correlation kernel, a constraint density, a projection-parameter measure, and projection kernels, we define a distancesurrogate, a regularised inverse operator, and a spectral dimension. The metricreconstruction statement is Euclidean-section only for the locked Gaussian instantiation; Lorentzian causal language is licensed only after a declared static or stationary analytic continuation and a compatible principal-symbol check. The prediction set contains a smooth crossover in ds(ℓ) located at the calibrated profilescale κ = 0.80 ± 0.05, a spin-dependent ringdown law tc/M = κ(1 + 1−a2 ∗),a phenomenological negative scalar running αs = −0.012 ± 0.005, and propagation and EHT shadow null statements. Only αs is compared here with public realdata. A Cobaya/CAMB Markov-chain inference using Planck 2018 likelihoods givesαs =−0.0037±0.0069 with convergence diagnostic R−1 = 0.0079. The PCT valueand Planck posterior are compatible at 0.97σ; this is compatibility, not empiricalconfirmation. The paper does not claim ultraviolet completeness, intrinsic dynamics, or a Standard Model derivation