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, highlighted by the James Webb Space Telescope (JWST) discovery of mature, massive galaxies at redshift z > 5 that contradict classical growth timelines. This paper presents a fully background-independent, axiomatic framework based on State Relational Entropy (SRE) dynamics. Spacetime topology and gravitational coupling are derived as probabilistic, macro-scale emergences from decentralized bidirectional Mobius informational networks. By filtering live spectroscopic data from the DESI DR1 catalog, we replace phenomenological weights with a continuous, error-driven Topological Stiffness Matrix derived from measurement uncertainty. To resolve the numerical precision breakdown caused by non-linear micro-scale perturbations, we introduce an Adaptive Tikhonov Manifold Regularization operator into the processing chain. Our regularized pipeline reveals a purely emergent cosmological phase boundary localized at the deep-space horizon z_crit = 4.1605. The system establishes a dual-layer holographic mapping: the low-density near-field universe (z < 4.1605) undergoes holographic dimension degeneracy into a 2D state due to matter dilution, while the high-density primordial universe (z >= 4.1605) activates latent spatial dimensions, inducing a quantized dimensional fluctuation up to the permanent 4D ceiling. This outbreak triggers a dynamic, oscillatory leap of the effective gravitational constant G_eff within a stable envelope (0.85 <= G_eff/G_0 <= 1.15). This gravitational booster lowers the primordial Jeans mass threshold by approximately 65% and halves accretion timescales, offering a self-consistent topological resolution to the JWST cosmological crisis. Furthermore, this framework maps the cosmic expansion profiles directly to network routing latencies, completely eliminating the necessity for any dark energy fields.