{
  "schema_version": 1,
  "problem_number": "AIM-CONVEX_GEOMETRY-0026",
  "title": "Subgaussian Convex Bodies Need Not Have Subgaussian Projections",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Every centrally symmetric convex body is an orthogonal projection of a centrally symmetric convex body whose linear functionals have psi_2/L_2 ratio at most 2 sqrt(2), independently of dimension. The lift is the intersection of a Euclidean ball with a cylinder in a sufficiently large dimension. In particular, for every n >= 2 we give an explicit body C_n in R^(64n^2) with this bound whose n-dimensional coordinate projection is (1/2) B_1^n. The latter has psi_2/L_2 ratio at least sqrt(n+2)/(2 sqrt(2 log 2)). Thus dimension-free subgaussianity of uniform volume does not survive geometric projection. This gives a negative answer to the projection subquestion in Paouris's Problem 7 in the AIM list on algorithmic convex geometry. It does not address the zonoid subquestion. The bad directional constant of B_1^n is known prior work and is credited. AI-assisted, self-audited and unrefereed; no independent review, formal verification or absolute priority is claimed.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.MG",
    "math.PR",
    "math.FA"
  ],
  "keywords": [
    "AIM-CONVEX_GEOMETRY-0026",
    "subgaussian convex bodies",
    "orthogonal projections",
    "uniform volume",
    "Orlicz norms"
  ],
  "manuscript_version_date": "2026-10-18",
  "publication_date": "2026-10-18",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-18",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-convex-geometry-0026/",
  "pdf_url": "https://eulersolve.org/papers/aim-convex-geometry-0026/paper.pdf?v=bf93f0c5c5ae",
  "doi": "10.5281/zenodo.23449393",
  "zenodo_record_url": "https://zenodo.org/records/23449393",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The projection subquestion is answered negatively. The zonoid and general characterization questions in the original AIM record remain unresolved. The bad directional constant of the cross-polytope is known prior work and is credited. AI-assisted, self-audited and unrefereed; no independent review, formal certification or absolute priority claim.",
  "files": {
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      "sha256": "bf93f0c5c5ae38d1fb554aad4670a5eceb69cae54e966e2051d5a9bbffeb090e"
    },
    "source.zip": {
      "sha256": "de65f9404e85ee059c9c0b9da4d1c0f92ed8c2b7a407ee1bda90e760be83e5f6"
    },
    "verification_report.md": {
      "sha256": "c0b5cac04832194750419aaa5e5ef6cfb086078d124e7d3fdc2d29b5df9edca6"
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  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}