A Romero-Law Graph-Dynamical Cosmology Without an Action Principle: From Pre-Geometry to Low-z Benchmarks (with a Reproducible "Universe Factory")

This paper develops and benchmarks the Relational Zero State (RZS) framework as an action-free, graph-dynamical model for pre-geometric cosmology. The starting point is not a spacetime Lagrangian, but a weighted relational network (graph) and node fields updated by explicit rules constrained by a stability principle (“Romero Law”). A reproducible workflow (“Universe Factory”) is provided to generate synthetic universes on a laptop and to track phase-transition diagnostics such as component unification (percolation), global communication onset (spectral connectivity growth), and saturation (stability plateaus). A core requirement is low-redshift validation. Mechanisms intended to amplify early rare events must remain compatible with the established low- and intermediate-redshift large-scale-structure (LSS) phenomenology. To isolate the specific RZS statistical effect—symmetric heavy-tail amplification of rare peaks with minimal impact on the two-point sector—controlled surrogate tests are performed using BOSS DR12 LOWZ and CMASS power-spectrum targets (NGC/SGC) and multiple k-windows. Iterative amplitude-adjusted Fourier transform (IAAFT) surrogates hold the target two-point spectrum fixed by construction while varying only the one-point distribution. Across catalogs and parameter sweeps, the heavy-tail prescription keeps skewness consistent with zero, increases excess kurtosis, and boosts tail exceedance in the high-sigma regime, consistent with an even-order (trispectrum-like) signature rather than a two-point modification. All scripts, figures, and summary tables are included for reproducibility and direct scrutiny. Keywords: Relational Zero State; RZS; pre-geometric cosmology; graph dynamics; emergent spacetime; large-scale structure; BOSS DR12; LOWZ; CMASS; power spectrum; heavy-tailed statistics; kurtosis; rare peaks; IAAFT; trispectrum; covariance; reproducible research.