{
  "abstract": "Every data-driven equation discovery method assumes (implicitly and without verification) that the target system obeys a single governing law ($K{=}1$). Here we show that this assumption is the primary bottleneck limiting scientific discovery in multi-mechanism systems, and introduce Physical Law Ecology, a framework that makes $K^*$ (the number of coexisting independent mechanisms) itself the first quantity to be determined from data. The framework automatically mines a pool of topologically distinct candidate equations, constructs a continuous dominance weight field across parameter space, and discovers analytic evolution laws governing mechanism succession---with optional monotonicity constraints encoding irreversible physics. Across four unrelated systems (elastomer mechanics, pool boiling, galactic dynamics, and droplet evaporation), BIC consistently identifies $K^*{=}3$ independent governing topologies. Applied to 163 SPARC galaxies (3,269 spatially resolved measurements), the framework autonomously recovers three gravitational laws whose coexistence provides evidence against the single-universal-acceleration hypothesis of MOND ($p<10^{-34}$). In engineering applications, multi-law weighted prediction reduces error by 67-72\\% over single-equation baselines while retaining full interpretability. By establishing the determination of $K^*$ as the zeroth step of scientific discovery-prior to and independent of equation search---this work opens a direction orthogonal to existing symbolic regression: not finding better equations, but mapping the ecology of mechanisms that govern complex systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08536",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiongheng Bian"
    },
    {
      "name": "Xiangyu Cui"
    },
    {
      "name": "Ma Feng"
    },
    {
      "name": "Xiaoyan Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ptt86h64xr25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08536",
  "fulltext_url": null,
  "id": "1ptt86h64xr25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08536",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.GA"
    ],
    [
      "arxiv",
      "cs.SC"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7212012420",
  "pdf_url": "https://arxiv.org/pdf/2609.08536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ptt86h64xr25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2609.08536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08536"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery",
  "title_text": "Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/1ptt86h64xr25",
  "venue": "arXiv",
  "versions": []
}