Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 100-01. Finite angular cylinder covers below the half-area bound
Manuscript map · lines 4395–4404
OpenAI@2026-10-07#rem:oai-p-100-01
Authors: OpenAI. Family 100.
Title: Finite angular cylinder covers below the half-area bound.
Abstract: A regular tetrahedron admits a finite cylinder covering with compact triangular perpendicular bases whose total area is less than half its minimum orthogonal projection area. This disproves the half-area cylinder-covering conjecture. By affine invariance, the same construction gives a counterexample to the directionwise normalized half-bound for every nondegenerate tetrahedron.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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