Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 084-02. The dyadic case of the Erdős similarity conjecture
Manuscript map · lines 4115–4124
OpenAI@2026-10-07#rem:oai-p-084-02
Authors: OpenAI. Family 084.
Title: The dyadic case of the Erdős similarity conjecture.
Abstract: We construct a compact subset of the unit interval, of measure arbitrarily close to one, that contains no affine copy of the dyadic sequence ${}{2{}{-n}:n{}ge1{}}$. The conclusion holds for every translation and every nonzero real dilation, of either sign, proving the dyadic case of the Erdős similarity conjecture.
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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