{
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  "ref": "R1403",
  "content_hash": null,
  "slug": "bochner-riesz-conjecture-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: The conjecture is known in dimension two and in substantial higher-dimensional subranges derived from restriction and decoupling estimates. Exact unresolved remainder: The full sharp strong-type range in dimensions d≥3 remains open.",
  "relevance": "This is the dated publication status for the canonical target Bochner-Riesz conjecture in higher dimensions.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: The conjecture is known in dimension two and in substantial higher-dimensional subranges derived from restriction and decoupling estimates.\n\nThe exact unresolved remainder is: The full sharp strong-type range in dimensions d≥3 remains open.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove the uniform estimate throughout the stated d,p,δ range.\n- Or give parameters in the range and an L^p counterexample.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.researchgate.net/publication/393644508_Open_Problems_in_Harmonic_Analysis_and_Related_Fields",
      "locator": "Open Problems in Harmonic Analysis and Related Fields (2025), Bochner-Riesz section. Bochner-Riesz conjecture section"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.researchgate.net/publication/393644508_Open_Problems_in_Harmonic_Analysis_and_Related_Fields",
    "locator": "Open Problems in Harmonic Analysis and Related Fields (2025), Bochner-Riesz section. Bochner-Riesz conjecture section"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1402",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1400",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1401",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "bochner-riesz-conjecture",
      "title": "bochner riesz conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}