{
  "abstract": "The horizon symmetry construction of Haco, Hawking, Perry, and Strominger yield two Virasoro central charges 12J after a specified Wald-Zoupas correction. Turning that calculation into a black hole microstate theory requires separate control of nonlinear charge integrability, the allowed counter-term class, and quantum state multiplicities. We formulate exact local and global integrability tests, prove uniqueness of the counter-term coefficients within a one-parameter ansatz, and identify the quotient in which a physically meaningful uniqueness theorem must be stated. A coadjoint-orbit model supplies globally defined classical moment maps, while unitary highest-weight modules supply an explicit algebraic quantum realization for macroscopic positive angular momentum, neither construction is proved equivalent to the gravitational phase space. A character calculation shows why a single Virasoro representation, despite having the desired central charge, does not provide the required large-central-charge entropy. We derive a curvature improvement invisible to the constant mode, quantize a regulated area-boost corner polarization, and find a continuous kinematic spectrum with divergent Gibbs trace. Explicit local modular CFT spectra with identical central charges yield different finite-temperature entropies, demonstrating that the available symmetry and quantum consistency data do not select the microscopic theory. We give a conditional sufficiency theorem and a concrete sequence of calculations needed to establish a gravitational completion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28700",
  "author_total": 1,
  "authors": [
    {
      "name": "Sandi Setiawan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53xcw0jf0e4a3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28700",
  "fulltext_url": null,
  "id": "53xcw0jf0e4a3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28700",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.gen-ph"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223204709",
  "pdf_url": "https://arxiv.org/pdf/2610.28700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53xcw0jf0e4a3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.28700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28700"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "Towards a Complete Kerr Soft-Hair Theory: Integrability, Counterterm Equivalence,and Quantum State Counting",
  "title_text": "Towards a Complete Kerr Soft-Hair Theory: Integrability, Counterterm Equivalence,and Quantum State Counting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/53xcw0jf0e4a3",
  "venue": "arXiv",
  "versions": []
}