Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 243-01. Choiceless polynomial time with counting does not capture polynomial time
Manuscript map · lines 7245–7254
OpenAI@2026-10-07#rem:oai-p-243-01
Authors: OpenAI. Family 243.
Title: Choiceless polynomial time with counting does not capture polynomial time.
Abstract: We prove that choiceless polynomial time with counting does not capture polynomial time on unordered finite structures, confirming the noncapture conjecture of Blass, Gurevich and Shelah. A linear-consistency query over 𝔽3 in a fixed binary vocabulary is decidable in polynomial time but not in the full counting formalism.
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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