OpenAI reports a cylinder-covering counterexample for a regular tetrahedron

A regular tetrahedron has a finite cylinder cover with compact triangular perpendicular bases whose total area is strictly less than half its minimum orthogonal projection area.

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Understanding the problem

Read the background

A regular tetrahedron has a finite cylinder cover with compact triangular perpendicular bases whose total area is strictly less than half its minimum orthogonal projection area.

Why it matters

If correct, disproves the half-area cylinder-covering conjecture using a regular tetrahedron.

What counts as progress

Must a cylinder cover cost at least half the minimum projection area of a convex body?

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