{
  "schema_version": 1,
  "problem_number": "AIM-ANALYSIS-0089",
  "title": "Sharp Induced-Norm Paving for Symmetric Weighing Matrices",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For real symmetric zero-diagonal weighing matrices W with W^2=dI, we deduce induced-l_p epsilon-paving into at most ceil(36 epsilon^(-q)) parts, where q=min(p,p') and q=1 at the endpoints. The exponent q is optimal uniformly over symmetric conference matrices. The elementary compression estimate ||W[S]||_p <= ||W[S]||_2^(2/q) transfers the published Ravichandran--Srivastava Hilbert multi-paving theorem; a single spectral paving also gives quantitative bounds for every p simultaneously. The matching lower order follows from classical Paley conference matrices. This short, theorem-dependent note proves a precise special case, not the general arbitrary-matrix induced-norm paving question. It is self-audited and unrefereed; the observation may be folklore and no absolute priority is asserted.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.FA",
    "math.CO"
  ],
  "keywords": [
    "induced operator norm",
    "paving",
    "weighing matrices",
    "conference matrices",
    "multi-paving",
    "interpolation",
    "Paley construction",
    "AIM-ANALYSIS-0089",
    "math.FA",
    "math.CO"
  ],
  "manuscript_version_date": "2026-09-29",
  "publication_date": "2026-09-29",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-09-29",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-analysis-0089/",
  "pdf_url": "https://eulersolve.org/papers/aim-analysis-0089/paper.pdf?v=dca311e5875d",
  "doi": "10.5281/zenodo.23025788",
  "zenodo_record_url": "https://zenodo.org/records/23025788",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof for real symmetric zero-diagonal weighing matrices, with matching exponent on the conference subclass; not closure of arbitrary-matrix induced-norm paving. The fixed-p optimal partition count and a common spectral partition giving bounds for all p are distinct statements. Published Hilbert multi-paving and classical Paley constructions are credited. This short theorem-dependent corollary is self-audited and unrefereed, with low novelty confidence; folklore and prior art are not excluded. No independent certification, formal verification or absolute priority is claimed.",
  "files": {
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      "sha256": "dca311e5875d7c5617a63fa388b19d88fb58dab7a3bb2cba973651b55f751fbe"
    },
    "source.zip": {
      "sha256": "5bba50d822d3652b10a7d0a8b8220a3bb0cc85e5ab45ab527d8f89673279f55c"
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    "verification_report.md": {
      "sha256": "199ec394fdbb93bdaba7fcfc5b23787086cab1d77d3a3d76f24d512362236e00"
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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."
}