{
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  "ref": "R1295",
  "content_hash": null,
  "slug": "convex-polygon-diagonal-intersection-asymptotic-status-20260801",
  "type": "claim",
  "title": "Current checked status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-27. The MathOverflow page has zero answers. Poonen and Rubinstein establish the n^4/24 leading term for regular polygons, while the checked searches found no proof that arbitrary convex polygons cannot create asymptotically more concurrence.",
  "relevance": "Records the strongest checked neighboring results and the exact remainder future work must settle.",
  "relevance_source": "recorded",
  "body": "A dated independent review on 2026-08-01 checked the structured sources below, the complete visible source discussion, exact-title and equivalent-formulation searches, and the current TheoremDB corpus. On 2026-07-27 the Stack Exchange API reported zero answers, no accepted answer, and no closure for question 212361; comments provide small values and candidate point sets only. Poonen and Rubinstein, SIAM Journal on Discrete Mathematics 11 (1998), compute regular-polygon intersections and give n^4/24+O(n^3), which supplies the current upper construction for f(n). OEIS A230281 records the least known values only for small n. Exact-title and asymptotic searches did not locate a later matching lower bound. A TheoremDB search for convex polygon diagonal concurrency, distinct interior intersections, and the n^4/24 asymptotic found no duplicate.\n\nA complete resolution must satisfy: Prove that f(n)/(n^4) tends to 1/24, or disprove the assertion by giving a different asymptotic bound separated from 1/24. A disproof by constructions must specify convex coordinates and prove the claimed count or asymptotic count of distinct concurrence points; a proof must control arbitrary multiple concurrences.",
  "status": "reported",
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  "scope": null,
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    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/212361/minimal-number-of-intersections-in-a-convex-n-gon",
      "locator": "Dataset references and independent 2026-08-01 status search."
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  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/212361/minimal-number-of-intersections-in-a-convex-n-gon",
    "locator": "Dataset references and independent 2026-08-01 status search."
  },
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      "slug": "convex-polygon-diagonal-intersection-asymptotic",
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