Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 112-01. Beyond the Square-Root Exponent for Depth-Three Boolean Circuits
Manuscript map · lines 4645–4654
OpenAI@2026-10-07#rem:oai-p-112-01
Authors: OpenAI. Family 112.
Title: Beyond the Square-Root Exponent for Depth-Three Boolean Circuits.
Abstract: We construct a language in deterministic polynomial time whose n-bit membership function requires $2{}{{}omega({}sqrt n)}$ gates in an unbounded-fan-in OR–AND–OR circuit. The bound holds at every sufficiently large input length and counts all gates, including the bottom layer.
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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