Recursive Correlations

Recursive Correlations are the correlations between parts of the substrate whose growth increases system-wide information content and so drives emergence. The book introduces them through Mutual Information Growth, dI≍/dt = (1/①⥂⧗⌂) × Σ_{i,j} R_{ij} × log₂(R_{ij}/(R_i × R_j)) · ℨᵇ, where R_i and R_j are the marginal correlations for indices i and j and t is time; this growth describes how Recursive Correlations raise information content under Information Conservation principles. Correlations themselves act as engines of emergence, amplifying systemic order from noise, and each phase of the Emergence Timeline Sequence, from fluctuations to ignition, marks a step in the upward sweep of correlation and recursion. The book states a testable prediction: non-Gaussian statistics in the cosmic microwave background from this information growth, detectable with sensitivity better than 10⁻⁶ through higher-order statistical analysis of temperature and polarization maps. It connects to Mutual Information Growth, Information Conservation, Emergence Timeline Sequence, Recursive Correlation Function and Recursive Defect Networks.