Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 084-01. The geometric case of the Erdős similarity conjecture
Manuscript map · lines 4105–4114
OpenAI@2026-10-07#rem:oai-p-084-01
Authors: OpenAI. Family 084.
Title: The geometric case of the Erdős similarity conjecture.
Abstract: We prove the geometric-progression case of the Erdős similarity conjecture. For every fixed $q{}in(0,1)$ and every ${}eta{}in(0,1)$, we construct a compact set $E_{q,{}eta}{}subseteq[0,1]$ of measure greater than $1-{}eta$ containing no nontrivial affine copy of ${}{q{}n:n{}ge1{}}$, for any translation and either sign of nonzero dilation. The set may depend on q; the result makes no simultaneous assertion for different ratios.
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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