Makeev's conjecture on universal cover

Precise 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 $U_n$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT 5.6 Pro

AI found the counterexample in dimensions 4 and 5 and wrote the paper and code without human mathematical input.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

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.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-10

   Counterexamples to Makeev's regular-simplex conjecture in dimensions four and five

   Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.