Formal-Causation Imprint on Large-Scale Structure: A Cahn–Hilliard Template, Observational Upper Limits, and DESI Forecasts

What is this? This paper asks a simple question: does Aristotle's "formal cause" leave a measurable fingerprint on the large-scale structure of the universe? We translate the concept of formal causation — the idea that structure-giving principles actively shape physical systems — into a single quantitative parameter λ (lambda), and then search for its signature in the cosmic matter distribution. What we did Built a prediction. We ran a Cahn–Hilliard phase-field simulation to model how formal causation would shape cosmic-web morphogenesis, producing a characteristic spectral bump at scale k_c = 0.096 h/Mpc. Searched for it. Using a pre-declared, blinded protocol with look-elsewhere correction (5,000 Monte Carlo trials), we scanned BOSS-calibrated power spectrum residuals for any deviation from ΛCDM. Found nothing — and that's a result. No statistically significant signal was detected (global p = 0.92). The constraint λ < 0.017 (95% CL) — equivalent to |ΔG_eff/G| < 1.1% If formal causation modulates gravity across the cosmic web, it does so by less than 1.1%. Important caveat The present analysis uses a BOSS-calibrated error model (not the full DR12 covariance matrix). All analysis parameters are pre-declared and frozen; a locked data-swap protocol for DR12 is defined in Appendix A of the manuscript. Think of this as a blinded analysis: methodology validated on realistic mocks before unblinding. What's in this repository File What it is 📄 formal_causation_v2.1.1_preprint.pdf Start here — the full paper (8 pages) 📊 results_pipeline.csv Every number in every table, machine-readable 🔬 gen_figures.py Run python gen_figures.py to reproduce all figures and results from scratch 📝 manuscript_v2.tex LaTeX source (revtex4-2 / PRD format) 🖼️ fig1–fig6_*.pdf All six publication figures Reproducibility pip install numpy matplotlib python gen_figures.py Fixed random seed (2024). Deterministic. All paper numbers flow from this single script. What's next DESI Year-1 data will push the sensitivity to λ < 0.011, probing sub-percent gravitational modulation across the entire cosmic web.