What was already known
Kuperberg proved the equivalent odd-function assertion in dimension three; the higher-dimensional geometric question remained open.
AI involvement
The manuscript credits ChatGPT as author of the construction and certificate generator. It reports no human mathematical input, but the prompting history is not independently documented.
ChatGPT is credited as author of the construction and certificate generator. The available source does not establish the level of independence required for AI-autonomous.
Importance
Gives counterexamples in the first two unresolved dimensions.
Limitations
The reported exact Magma run checks the dimension-five algebraic transversality step. The dimension-four certificate run and common analytic reductions lack documented completed checks; dimensions six and above are outside the claim.
Technical verification
The source reports an independent human run of an exact Magma unit-ideal certificate for the dimension-five algebraic transversality step. Dimension four has a written direct proof and an unreported optional certificate run; no completed check of the common analytic argument is documented.
Independent checking
The dimension-five tensor ideal is the unit ideal, the algebraic transversality step used in the d=5 counterexample. Exact rational Gröbner-basis computation with IsProper asserting false
- Checker
- Magma, run by an unnamed human verifier
- Scope
- The dimension-five tensor ideal is the unit ideal, the algebraic transversality step used in the d=5 counterexample
- Basis
- Reported by the linked checker
Human understanding
The documented human action is running a certificate, with no human account of the central geometric and variational mechanism. Few is the evidence default.
Correction and publication history
Reports explicit four- and five-dimensional counterexamples to Makeev’s conjecture.
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