{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1124",
  "content_hash": null,
  "slug": "pierce-expansion-upper-exponent-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-31. Chase and Pandey prove \\(L(N)=O_\\varepsilon(N^{1/3-2/177+\\varepsilon})\\). The dated search did not find a larger published saving, so this record asks for a strict improvement over that theorem. Exhibit a fixed \\(\\delta>2/177\\) and prove that for every \\(\\varepsilon>0\\) there is a constant \\(C_\\varepsilon\\) with \\(L(N)\\le C_\\varepsilon N^{1/3-\\delta+\\varepsilon}\\) for every \\(N\\ge2\\).",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-07-31. Chase and Pandey prove \\(L(N)=O_\\varepsilon(N^{1/3-2/177+\\varepsilon})\\). The dated search did not find a larger published saving, so this record asks for a strict improvement over that theorem.\n\nA complete resolution must satisfy this condition: Exhibit a fixed \\(\\delta>2/177\\) and prove that for every \\(\\varepsilon>0\\) there is a constant \\(C_\\varepsilon\\) with \\(L(N)\\le C_\\varepsilon N^{1/3-\\delta+\\varepsilon}\\) for every \\(N\\ge2\\).",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/164129/improving-known-bounds-for-pierce-expansions-cash-prize",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/164129/improving-known-bounds-for-pierce-expansions-cash-prize",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "relations": [
    {
      "slug": "R1123",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "pierce-expansion-upper-exponent",
      "title": "pierce expansion upper exponent",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}