Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 100-03. Slope-field perturbations of the two-cylinder covering
Manuscript map · lines 4415–4424
OpenAI@2026-10-07#rem:oai-p-100-03
Authors: OpenAI. Family 100.
Title: Slope-field perturbations of the two-cylinder covering.
Abstract: The two-cylinder covering of a regular tetrahedron can be perturbed to give finite covers with total perpendicular base area strictly below half its minimum projection area. These covers give negative answers to both the half-area question and the directionwise normalized half-bound conjecture. By affine invariance, the directionwise conclusion holds 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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