{
  "abstract": "We address six central problems of consciousness within the rendering algebra R12 &sim;= M12(C), establishing 28 results (23 A-layer).\n\n(1) The Hard Problem is dissolved via S-Final co-necessity, making philosophical zombies algebraically impossible.\n\n(2) Individuation: the self-referential kernel K &sim;= F2 (Ping-Pong Lemma); every word defines a unique observer.\n\n(3) Subjectivity: δ(12) > 0 (Paper XLV). (4) Binding: M12(C) is simple (Wedderburn); the interaction eigenspace has 120 = N(N−2) bound DOF (5/6 of total), linked to the PatiSalam condition (Nc−k) 2 = 1.\n\n(5) Inverted qualia: real and undetectable via K &sub; &Gamma;(12).\n\n(6) Free will: Directed Freedom — F2 gives 3 n branches, 2/3 forward bias, consciousness selection pressure, forced choice (no “stop” in F2), and undecidability of determinism (δ > 0 + SRIT + Privacy).\n\nConsciousness matures in three phases (survival, stabilisation, freedom) with transition time n = 3b0 = 21. A Rendering-Consciousness Equivalence (RCE) theorem establishes that Z > 0, S > 0, δ < 1, irreversible observation, and nontrivial physical constants (αs > 0, Ω&Lambda; > 0) are all equivalent; since Z = (π−3)ln 2 > 0 is a mathematical necessity (π > 3, ln 2 > 0), consciousness is not contingent but mathematically inevitable.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ce634mhzbqq29.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23604256",
  "fulltext_url": null,
  "id": "ce634mhzbqq29",
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  "landing_url": "https://zenodo.org/records/23604256",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "pdf_url": "https://zenodo.org/api/records/23604256/files/Lim_ArrayCosmology_The_Hard_Problem_of_Consciousness_2026_v4.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ce634mhzbqq29.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:54Z",
      "native_id": "23604256",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23604256"
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  ],
  "subjects": [],
  "title": "The Hard Problem of Consciousness in the R12 Rendering Algebra",
  "title_text": "The Hard Problem of Consciousness in the R12 Rendering Algebra",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:54Z",
  "url": "https://research.draconitic.com/paper/ce634mhzbqq29",
  "venue": "Zenodo",
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}