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 pregeometric
framework in which a two-point correlator on a primitive measurable space can
define metric and causal structures only where explicit admissibility assumptions
hold. Starting from a positive semi-definite correlation kernel, a constraint den
sity, a projection-parameter measure, and projection kernels, we define a distance
surrogate, a regularised inverse operator, and a spectral dimension. The metric
reconstruction statement is Euclidean-section only for the locked Gaussian instan
tiation; Lorentzian causal language is licensed only after a declared static or sta
tionary analytic continuation and a compatible principal-symbol check. The pre
diction set contains a smooth crossover in ds(ℓ) located at the calibrated profile
scale 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 propaga
tion and EHT shadow null statements. Only αs is compared here with public real
data. A Cobaya/CAMB Markov-chain inference using Planck 2018 likelihoods gives
αs =−0.0037±0.0069 with convergence diagnostic R−1 = 0.0079. The PCT value
and Planck posterior are compatible at 0.97σ; this is compatibility, not empirical
confirmation. The paper does not claim ultraviolet completeness, intrinsic dynam
ics, or a Standard Model derivation