The Recursive Universe: A Renormalization Framework for Cosmic Complexity

We present a unified theoretical framework that integrates causal emergence theory with a Bayesian critique of cosmological exceptionalism. The Causal Renormalization Group (CRG) treats Effective Information as a scale-dependent running coupling, defining the Causal Beta Function, β_C(λ), as the derivative of causal power with respect to coarse-graining scale. This formalism classifies systems by their causal flow topology: reductionist systems exhibit monotonic decay (β_C < 0), while emergent systems display regimes of positive flow (β_C > 0).

We introduce the distinction between Structural Assembly (A_S) and Network Assembly (A_N) to resolve the "Substrate Confusion" underlying the apparent Complexity Ridge at biological scales. The Generative Continuity Postulate, combined with a Maximum Entropy prior over observer locations, yields a posterior probability approaching unity for unobserved higher-order causal layers.

The framework predicts a resurgence of causal power at astrophysical scales driven by gravitational network topology, reframing humanity as a functional substrate within an indefinitely recursive hierarchy rather than the apex of cosmic complexity. We derive four testable predictions: spin chirality correlations at 200 Mpc scales, entropy deficits in cosmic voids, technosignature waste-heat excess, and characteristic patterns in the Causal Beta Function across scales. While individual anomalies may admit alternative explanations, their joint detection would strongly favor recursive structuring over standard cosmological models.