{
  "abstract": "FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's state — but current formalizations face a fundamental tension between information loss and integration, with algorithmic information theory offering a lossless alternative. | MATH: IIT 4.0 defines Φ via the *Earth mover's distance* (Wasserstein metric) between the cause-effect repertoire of a mechanism and its partitioned counterpart: Φ = min_partition W( p(mechanism_state) || p(partitioned_state) ). Tononi's original (2008) formulation used effective information: EI(X→Y) = H(Y) − H(Y|X) summed over minimal partitions. The algorithmic alternative (arXiv:1405.0126) replaces Shannon entropy with Kolmogorov complexity: Φ_AIT = K( system_state ) − Σ K( subsystem_states ), requiring no lossy compression. | CONNECTION: The Wasserstein metric is a *transportation* distance — its optimal solution on discrete state spaces corresponds to a linear programm\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/828hrw98me3bq.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526314",
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  "id": "828hrw98me3bq",
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  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/828hrw98me3bq.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:49Z",
      "native_id": "23526314",
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  "title": "IIT 4.0's Phi: Wasserstein Metric and the Integration-Information Tradeoff — E8 Intelligence Research",
  "title_text": "IIT 4.0's Phi: Wasserstein Metric and the Integration-Information Tradeoff — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:49Z",
  "url": "https://research.draconitic.com/paper/828hrw98me3bq",
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