{
  "schema_version": 1,
  "problem_number": "AIM-FUNCTIONAL_ANALYSIS-0027",
  "title": "Forcing Absoluteness of Minimal and Maximal C∗-Tensor Products",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We answer an AIM question about whether the minimal or maximal C*-tensor product commutes with forcing. We use the standard convention that a ground-model C*-algebra is replaced in the extension by the metric completion of its old normed *-algebra. Under this convention, both ⊗_min and ⊗_max commute canonically with every set-forcing extension, for arbitrary ground-model factors; no separability, density-character, or cardinal-preservation hypothesis is needed. The minimal case follows by extension of faithful spatial representations. For the maximal case, any putative larger new norm would give finitely satisfiable old semialgebraic C*-seminorm constraints. Quantifier elimination for real closed fields and compactness inside the ground model then produce an old C*-seminorm exceeding the old universal norm, a contradiction.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.OA",
    "math.LO"
  ],
  "keywords": [
    "C*-algebras",
    "tensor products",
    "set forcing",
    "absoluteness",
    "real closed fields",
    "C*-tensor product",
    "forcing",
    "maximal tensor norm",
    "real closed field",
    "AIM-FUNCTIONAL_ANALYSIS-0027",
    "open mathematics",
    "mathematical proof",
    "math.OA",
    "math.LO"
  ],
  "manuscript_version_date": "2026-09-01",
  "publication_date": "2026-09-02",
  "publication_date_kind": "first public online release",
  "version": "1.0 (typesetting revision 2026-09-05)",
  "date_modified": "2026-09-05",
  "presentation_revision_only": true,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-functional-analysis-0027/",
  "pdf_url": "https://eulersolve.org/papers/aim-functional-analysis-0027/paper.pdf?v=79a934b7d6ff",
  "doi": "10.5281/zenodo.22245547",
  "zenodo_record_url": "https://zenodo.org/records/22245547",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete for the explicit extension-completion convention reconstructed from the one-line AIM source.",
  "files": {
    "paper.pdf": {
      "sha256": "79a934b7d6ff6f32b877edac833af371fdef64c59d04520c9e1b6210dfc7e31e"
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    "source.zip": {
      "sha256": "f44dbd345a6b4d5ee33f5fce80a7283838352fead82141ef1f1209c87b2b9031"
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    "verification_report.md": {
      "sha256": "95d03bec78622328814cf717a641c24b45a180cef209697bbd16179b0a58632f"
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  },
  "ai_use_disclosure": "AI-assisted tools supported literature search, computation, proof auditing, and manuscript preparation. The author remains responsible for all claims and the final text."
}