Makeev's conjecture on universal cover
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Statement
Let be the difference polytope of a regular -simplex such that circumscribes a sphere of diameter 1. Then every set of diameter 1 in is covered by a rotated copy of .
Context
Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.
A named 1994 conjecture in metric geometry, recorded in the Handbook of Discrete and Computational Geometry's problem chapter, in the universal-covers tradition of Lebesgue's problem. Real and thirty-two years old, but specialist: level with the named specialist band at 15.
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AI found the counterexample in dimensions 4 and 5 and wrote the paper and code without human mathematical input.
Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.
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0 human reviews · 0 machine checksNo person has reviewed this attempt. It has not been checked at all.
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