A Game-Theoretic Framework for Hierarchical Structure Formation: Bayesian Inference, Spectral Stability, and Emergent Scaling

A Game-Theoretic Framework for Hierarchical Structure Formation: Bayesian Inference, Spectral Stability, and Emergent ScalingData, Code, and Reproducibility Archive This repository contains all data, analysis code, and documentation for the research manuscript “A Game-Theoretic Framework for Hierarchical Structure Formation.” The study presents a unified dynamical model where supermassive black holes and host galaxies act as strategic agents in a non-cooperative game with empirically constrained payoff functions. Key Findings: · Bayesian-inferred parameters from SDSS data (α=2.15±0.03, β=0.95±0.04, γ=0.58±0.02), achieving R²=0.78 in star formation rate prediction.· Spectral stability proof via Implicitly Restarted Arnoldi Method (IRAM), confirming asymptotic stability (all Re(λᵢ) < 0).· Dual-attractor structure: gas-poor relaxed systems converge toward r≈√2≈1.414 (geometric packing), while gas-rich active systems exhibit r≈φ≈1.618 (golden ratio, growth optimization).· Cross-validation via Dynamic Mode Decomposition (DMD) and neural adjoint methods.· Observational predictions for JWST, Rubin Observatory, and Euclid. Contents: · /data/: Processed SDSS (MPA-JHU DR7), Local Group, Virgo, Coma, Fornax, and Perseus cluster catalogs· /code/: Full Python pipeline (PyMC3, PyTorch, SciPy) for Bayesian inference, IRAM, DMD, bootstrap analysis, and visualization· /notebooks/: Jupyter notebooks for reproducibility and interactive exploration· /manuscript/: LaTeX source and PDF of the manuscript· /figures/: All publication-ready figures· environment.yml and requirements.txt: Exact computational environment specifications