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  "problem_id": "vibemathed:makeev-s-conjecture-on-universal-cover",
  "title": "Makeev's conjecture on universal cover",
  "canonical_statement": "Let $U_n\\subset\\mathbb R^n$ be the dual of the difference polytope of a regular $n$-simplex such that $U_n$ circumscribes a sphere of diameter 1. Then every set of diameter 1 in $\\mathbb R^n$ is covered by a rotated copy of $U_n$.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-08-10T00:00:00.000Z",
      "title": "Counterexamples to Makeev's regular-simplex conjecture in dimensions four and five",
      "summary": "Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.",
      "ai_contribution": "ai_discovered",
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        "vibemathed:makeev-s-conjecture-on-universal-cover:attempt"
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      "attempted_at": "2026-08-10T00:00:00.000Z",
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      "outcome": "AI found the counterexample in dimensions 4 and 5 and wrote the paper and code without human mathematical input.",
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          "label": "Python and Magma code",
          "url": "https://github.com/simplex4/math-results/tree/main/makeev-code/a4",
          "kind": "code",
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        },
        {
          "label": "Conjecture 21.3.2",
          "url": "https://www.csun.edu/~ctoth/Handbook/chap21.pdf",
          "kind": "problem-record",
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        },
        {
          "label": "Makeev's conjecture",
          "url": "https://arxiv.org/abs/math/9809165v3",
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          "label": "Counterexamples to Makeev's regular-simplex conjecture in dimensions four and five",
          "url": "https://github.com/simplex4/math-results/blob/main/makeev-code/a4/makeev_d4_d5.pdf",
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      "note": "Checked by this site on 17 August 2026: the repository is real and unusually substantial - 596 files across four independently-built verification approaches (Magma certificates, interval-arithmetic C++, tensor-polynomial certificates, Python numerics), plus the full prompts and chat transcripts, and the problem-record links verify (Makeev's conjecture in arXiv:math/9809165, Handbook chapter 21). The certificates were not run here. The submitter reports a preliminary check by two students, which is private checking, not independent review - Unreviewed stands.",
      "sources": [
        {
          "label": "VibeMathed: Makeev's conjecture on universal cover",
          "url": "https://vibemathed.com/problem/makeev-s-conjecture-on-universal-cover",
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          "label": "Counterexamples to Makeev's regular-simplex conjecture in dimensions four and five",
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  "sources": [
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      "label": "Counterexamples to Makeev's regular-simplex conjecture in dimensions four and five",
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    "VibeMath has not independently verified the mathematical claim.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}