Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 182-03. A power saving for square-difference-free sets
Manuscript map · lines 5735–5744
OpenAI@2026-10-07#rem:oai-p-182-03
Authors: OpenAI. Family 182.
Title: A power saving for square-difference-free sets.
Abstract: We prove that there are absolute constants c > 0 and C < ∞ such that every set $A{}subseteq{}{1,{}ldots,N{}}$ with no nonzero square difference satisfies $|A|{}le C N{}{1-c}$. This answers the fixed-power question posed by Green and Sawhney.
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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