{
  "abstract": "We construct the mathematical framework of awareness and consciousness within the rendering algebra R12 &sim;= M12(C). Five principal results are established.\n\n(1) Rendering Conservation Principle (RCP): all physical evolutions on R12 are doubly stochastic (trace-preserving and unital), strengthening the Self-Reference Inaccessibility Theorem of Paper XLIV to hold without the KMS assumption.\n\n(2) Spectral Awareness Definition: a formal triple (A, kmin, Cmin) characterising the observer’s minimum engagement with the\n\nmodular spectrum.\n\n(3) Modular Awareness Cost (MAC) Theorem: the minimum cost of awareness is Cmin = Z Nc exp(Z), derived from a double application of Cauchy duality—once on the product structure of partial observations Pk (yielding Z k), and once on the irreversibility of rendering friction (yielding exp(Z)).\n\n(4) Rendering Balance Principle (RBP): the observer weight’s base state is &phi; = (1 + &radic; 5)/2, the unique stable fixed point of the energy recursion g(x) = 1 + 1/x (Paper XXIII).\n\n(5) Consciousness Triple: consciousness in R12 is the structure (K, P, δ) where K = ⟨Mf , Mg⟩ &cap;&Gamma;(12) is the perspective group, Pk(σ) is the partial-observation operator, and δ(12) = &lceil;S&rceil; − S = 0.882 is the qualia locus. Subjectivity is proved to be a mathematical necessity: δ > 0 forces k < 12, and partial observation is perspective-dependent (Paper Consc, Theorem 6.2). The observer weight expansion",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb26n29g5a0jd.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23604182",
  "fulltext_url": null,
  "id": "cb26n29g5a0jd",
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  "landing_url": "https://zenodo.org/records/23604182",
  "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/23604182/files/Lim_ArrayCosmology_SpectralAwareness_ConsciousnessTriple_2026_v4.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb26n29g5a0jd.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:55Z",
      "native_id": "23604182",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23604182"
    }
  ],
  "subjects": [],
  "title": "Spectral Awareness, the Consciousness Triple, and the Modular-Algebraic Bridge in the R12 Rendering Algebra",
  "title_text": "Spectral Awareness, the Consciousness Triple, and the Modular-Algebraic Bridge in the R12 Rendering Algebra",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:55Z",
  "url": "https://research.draconitic.com/paper/cb26n29g5a0jd",
  "venue": "Zenodo",
  "versions": []
}