{
  "abstract": "This work develops the physical celestial Clebsch–Gordan transform of a radiative two-particle Bose sector and establishes its intrinsic source-identification properties together with an obstruction to bounded Hilbert-space completion of the retained angular transform.\n\nFor every physical external-label pair, the intrinsic cross-ratio transform and its unitary full signed principal-series continuation are injective on the intrinsic physical source range generated by the ordered separable pair core. The proof retains the complete unequal-label source character and combines source-pair coarea, Gaussian and harmonic testing, Abel–Fresnel reduction, shifted Mellin factorization, explicit beta-function evaluation, and logarithmic-cylinder Fourier uniqueness. The physical beta coefficient is nonzero for every external-label pair, integer angular mode, and real Mellin frequency, establishing recovery of the original source from complete intrinsic celestial data.\n\nThe retained angular transform exhibits a separate analytic obstruction. An explicit sequence of finite-rank physical sources at fixed opposite-helicity external labels has uniformly bounded source Hilbert norms while its normalized retained-output norms diverge. The proof uses the physical cross-ratio kernel, an explicit coherent-output lower bound, exact zero-spin frequency reflection, Plancherel normalization, and a same-input retained-output comparison. Consequently, the retained transform admits no bounded extension to the original full fixed-input source Hilbert space at these labels. Finite-window continuity establishes failure of a common almost-everywhere decomposable bound on positive-measure external-label neighborhoods. The obstruction persists under the specified compact-smooth angular and log-energy source constructions.\n\nThese results preserve the source-aware Weyl representation geometry and establish intrinsic source faithfulness independently of bounded completion. The retained coefficient determines a closed graph relation and a canonical output-ambiguity quotient, while single-valued closability and a physically adequate replacement operator domain remain open.\n\nThe mathematical conclusions distinguish exact source identifiability from bounded retained-output continuity. They do not establish a bounded inverse, a uniform lower frame bound, injectivity on the entire completed source Hilbert space, or injectivity after retained fundamental-sheet projection. The principal results and their analytic foundations are accompanied by machine-checked Lean formalizations, with theorem-level provenance and verification records identified in the manuscript.",
  "abstract_shown": true,
  "affiliations": [
    "Institute Lux Consilio"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Zed James",
      "orcid": "0009-0000-2120-0739"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ft10x6g3x2p4b.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23509540",
  "fulltext_url": null,
  "id": "ft10x6g3x2p4b",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23509540",
  "language": "eng",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23509540/files/The%20Physical%20Celestial%20Clebsch-Gordan%20Transform%20of%20a%20Radiative%20Bose%20Pair%20v2.0.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ft10x6g3x2p4b.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:33Z",
      "native_id": "23509540",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23509540"
    }
  ],
  "subjects": [],
  "title": "The Physical Celestial Clebsch–Gordan Transform of a Radiative Bose Pair",
  "title_text": "The Physical Celestial Clebsch–Gordan Transform of a Radiative Bose Pair",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:33Z",
  "url": "https://research.draconitic.com/paper/ft10x6g3x2p4b",
  "venue": "Zenodo",
  "versions": []
}