"Unified Recursive Emergence Theory (URET): A Depth‑Limited Quadratic Map Linking Quantum, Neural, and Cosmic Energy Patterns" (Concise, descriptive, and clearly signals the novel bridge across physical scales.)

The Unified Recursive Emergence Theory (URET) posits a common mathematical framework, potentially rooted in quadratic map dynamics (z -> z^2 + c), governing the emergence of complexity across quantum, neural, and cosmic scales. This study presents an initial computational validation of URET by testing the hypothesis that complexity parameters derived independently from these domains exhibit correlations when analyzed through this dynamical system. We derived complexity parameters c_q (quantum), c_n (neural), and c_c (cosmic) from publicly available datasets (Zenodo particle data, MICA-PNI 7T fMRI, SDSS DR8 filaments), obtaining c_q=0.171, c_n=1.066, and c_c=0.507. Using these parameters, we iterated the quadratic map for N=1000 initial seeds, calculating energy moments M_d(z0, c) with numerical guardrails. Pearson correlations (ρ) between moment lists were computed and compared against cubic and logistic-like map null models. A strong, statistically significant positive correlation was found between the quantum and cosmic domains (ρ_qc = 0.645, p < 0.001, n=195), potentially supporting a URET-predicted link. However, severe numerical instability, particularly associated with c_n, rendered correlations involving the neural domain (ρ_qn, ρ_nc) inconclusive (based on n=6 and n=11 valid points, respectively). While the quadratic map showed more specificity than null models, significant limitations include the instability, the use of substitute datasets, and the interpretation of parameter extraction methods. This work provides tentative support for the URET q-c link, but further research is required to address stability and refine the methodology. LicenseManuscript © 2025 Allen Wagner — Creative Commons BY 4.0.Code — MIT License.Unified Recursive Emergence Theory, URET, complexity, emergence, quadratic map, dynamical systems, quantum physics, neuroscience, cosmology, computational validation, correlation analysis, open data.