{
  "abstract": "The S-Final principle of Array Cosmology requires Ωreal + Ωimag = 0, where Ωreal = +1 corresponds to the rendered physical universe. This paper characterises the complementary object X responsible for Ωimag = −1 without defining it as “consciousness” or any other pre-theoretic concept. Ten theorems are proved from the R12 rendering algebra alone:\n\n(1) X = −1 is the unique central involution satisfying the S-Final trace condition;\n\n(2) X exists if and only if matter exists;\n\n(3) the coupling κ = &Sigma;(s)&Gamma;(γ) factorises uniquely into a universal signal and a local receiver;\n\n(4) &Gamma;(γ) > 0 for all γ ≥ 0 (non-annihilation);\n\n(5) the self-reference residual δ(12) > 0 (incompleteness), certified by the interval S &isin; (1/9,1/8);\n\n(6) partial observation is perspective-dependent while total observation is objective;\n\n(7) self-recognition requires exactly two rendering cycles (4π rotation);\n\n(8) the algebraic sign inversion B = −1 and the modular residual shift M12 f = 1 0 −12 1 are dual manifestations of the same self-referential monodromy;\n\n(9) the self-referential kernel K is infinite, non-abelian, and torsion-free, endowing the simple trace &tau;(X) = −1 with infinitely rich internal structure;\n\n(10) self-referential convergence requires 3 < π < 3 + 1/ln2, establishing an existence window. All ten results carry tier [A]; interpretive correspondences with consciousness, subjectivity, and qualia are registered at tier [C], explicitly separated from the mathematical content. Two open problems are posed: the individuation of X via the kernel K, and the\n\nconnection to integrated information theory",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1x4bjdd2p4tjr.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23603714",
  "fulltext_url": null,
  "id": "1x4bjdd2p4tjr",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23603714",
  "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/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23603714/files/Lim_ArrayCosmology_Consciousness_2026_v5.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1x4bjdd2p4tjr.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:57Z",
      "native_id": "23603714",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23603714"
    }
  ],
  "subjects": [],
  "title": "Consciousness in Array Cosmology: The Fractal Coupling Function, the Born-Rule Correction, and the Rung Tower of the R12 Rendering Algebra",
  "title_text": "Consciousness in Array Cosmology: The Fractal Coupling Function, the Born-Rule Correction, and the Rung Tower of the R12 Rendering Algebra",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:57Z",
  "url": "https://research.draconitic.com/paper/1x4bjdd2p4tjr",
  "venue": "Zenodo",
  "versions": []
}