Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 092-02. Translative covering densities of order n log n
Manuscript map · lines 4275–4284
OpenAI@2026-10-07#rem:oai-p-092-02
Authors: OpenAI. Family 092.
Title: Translative covering densities of order n log n.
Abstract: For every sufficiently large dimension n, we construct a centrally symmetric convex body whose translative covering density exceeds $c n{}log n$, where c > 0 is absolute. This disproves the existence of a universal linear upper bound and matches the order of Rogers' upper bound.
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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