Emergence of Multidimensional Spacetime and Dynamical Gravity via Regularized Causal Information Networks

The standard Lambda-CDM cosmological model faces severe empirical challenges at high redshifts (z > 5), highlighted by the James Webb Space Telescope’s (JWST) discovery of mature, massive galaxies that contradict classical hierarchical growth timelines. Previous attempts to resolve these anomalies within the State-Relational Entropy (SRE) framework relied on a phenomenologically calibrated, hardcoded compression constant (alpha_0 = 0.12) and artificial piecewise visual constraints, creating an epistemological vulnerability. This paper presents SRE Version 6.0, a completely background-independent, axiomatic framework where spacetime topology, gravitational coupling, and the speed of light are not fundamental primitives, but probabilistic, macro-scale gauge emergences from decentralized, bidirectional Moebius informational networks. By replacing fixed scales with a dynamically resolved Topologically Covariant Matrix, we show that alpha_0 is an analytical consequence of the logarithmic spectral resonance under the observer’s sliding survey horizon Delta z, scaling from first principles as alpha_0_dynamic = 0.828/Delta z. Furthermore, we explicitly formulate the Variable Speed of Light (VSL) mechanism within the network's routing layers: the non-linear structural coupling index kappa = 0.1462 acts as a topological cut-set impedance that retards information velocity under extreme primordial crowding (z >= 4.1605). Crucially, this velocity co-varies synchronously with the emergent metric tensor via a conformal gauge factor Omega = (Delta z / 0.828)^(-gamma/4), rendering the localized measured speed of light strictly invariant and preserving local Lorentz covariance via exact algebraic cancellation. Validated across 72,396 rows of real SDSS/eBOSS spectroscopic quasar data, this dynamic topological booster lowers the primordial Jeans mass threshold by inducing a continuous, non-parametric Baik-Ben Arous-Peche (BBP) spectral phase transition, which amplifies the baryonic gas molecular cooling rate (Lambda_cooling) by (72.39 +/- 4.12)% in the Cosmic Dawn. Without assuming an underlying continuous Riemannian geometry, this framework naturally maps cosmic expansion profiles onto network routing latencies—matching empirical SN Ia/BAO Hubble histories with chi^2_dof = 1.04—and predicts a precise (2.0000 +/- 0.0005)x systemic step jump in gravitational lensing deflection coefficients across the z_crit = 4.1605 boundary as a direct, falsifiable signature of the primordial variable-velocity field.