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"finished", "type": "image-tiles" }, "size": 0, "storage_class": "L" } }, "order": [], "total_bytes": 0 }, "metadata": { "copyright": "Copyright \u00a9 2026 Takayuki Takagi", "creators": [ { "affiliations": [ { "name": "Independent Researcher, Higashimatsuyama, Saitama, Japan" } ], "person_or_org": { "family_name": "Takagi", "given_name": "Takayuki", "identifiers": [ { "identifier": "0009-0003-5188-2314", "scheme": "orcid" } ], "name": "Takagi, Takayuki", "type": "personal" } } ], "description": "

What is this?

\n

This paper asks a simple question: does Aristotle's \"formal cause\" leave a measurable fingerprint on the large-scale structure of the universe?

\n

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.

\n

What we did

\n
    \n
  1. \n

    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.

    \n
    2. \n
  2. \n

    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.

    \n
    3. \n
  3. \n

    Found nothing — and that's a result. No statistically significant signal was detected (global p = 0.92).

    \n
    4. \n
\n

The constraint

\n
\n

λ < 0.017 (95% CL) — equivalent to |ΔG_eff/G| < 1.1%

\n
\n

If formal causation modulates gravity across the cosmic web, it does so by less than 1.1%.

\n

Important caveat

\n

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.

\n

What's in this repository

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
FileWhat it is
\ud83d\udcc4 formal_causation_v2.1.1_preprint.pdfStart here — the full paper (8 pages)
\ud83d\udcca results_pipeline.csvEvery number in every table, machine-readable
\ud83d\udd2c gen_figures.pyRun python gen_figures.py to reproduce all figures and results from scratch
\ud83d\udcdd manuscript_v2.texLaTeX source (revtex4-2 / PRD format)
\ud83d\uddbc\ufe0f fig1–fig6_*.pdfAll six publication figures
\n

Reproducibility

\n
pip install numpy matplotlib\npython gen_figures.py\n
\n

Fixed random seed (2024). Deterministic. All paper numbers flow from this single script.

\n

What's next

\n

DESI Year-1 data will push the sensitivity to λ < 0.011, probing sub-percent gravitational modulation across the entire cosmic web.

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