{
  "schema_version": 1,
  "problem_number": "OWR-1535-001",
  "title": "Proper Riesz Equilibrium Support on Connected Sets of Revolution",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For every 0<s<1, we construct a connected compact set of revolution whose Riesz s-equilibrium measure omits a positive-capacity circle of its outer boundary. The generating set can also be chosen connected with nonempty interior. This gives an affirmative answer to the existential support question posed by Brauchart, Hardin and Saff. The construction combines their large-radius negative-distance kernel with a uniform polygonal domination inequality on the unit disk. A strict potential gap gives exact support exclusion at finite radius. The proof does not determine the equilibrium measure and does not require a numerical minimization. This is an unrefereed preprint, with source comparison, self-audit and exact arithmetic diagnostics; no independent or formal verification or absolute priority certification is asserted.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "keywords": [
    "OWR-1535-001",
    "math.CA",
    "math.MG"
  ],
  "manuscript_version_date": "2026-10-21",
  "publication_date": "2026-10-23",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-23",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-1535-001/",
  "pdf_url": "https://eulersolve.org/papers/owr-1535-001/paper.pdf?v=2debf882a30f",
  "doi": "10.5281/zenodo.23586519",
  "zenodo_record_url": "https://zenodo.org/records/23586519",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For every real 0<s<1, a connected compact generating set strictly inside the right half-plane has a set of revolution whose Riesz s-equilibrium support omits a positive-capacity circle of its outer boundary. The generating set can have nonempty interior. A uniform polygonal distance-power gap and finite-radius strict domination prove exact exclusion. This answers the frozen existential question affirmatively, not the circular-torus, convexity or smoothness questions. Existing BHS reduction, limiting kernel and domination are credited; novelty and absolute priority are not certified. This is a self-audited, AI-assisted, unrefereed preprint. No independent certification, formal proof verification or absolute-priority claim is made.",
  "files": {
    "paper.pdf": {
      "sha256": "2debf882a30f402f2a71b8b177ee913438d414e0b089920837f316de8e1d9ece"
    },
    "source.zip": {
      "sha256": "05539d1c7e419fb0d3fe020c68f3062482704a3d3a3fcb452aceef65a2030c0d"
    },
    "verification_report.md": {
      "sha256": "658f1b82302857ff9cc47aa8f2224ef82e0858bdcd0f6a361621057a5b1d3f87"
    }
  },
  "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."
}