Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 243-02. Witnessed symmetric choice is strictly stronger than choiceless polynomial time with counting
Manuscript map · lines 7255–7264
OpenAI@2026-10-07#rem:oai-p-243-02
Authors: OpenAI. Family 243.
Title: Witnessed symmetric choice is strictly stronger than choiceless polynomial time with counting.
Abstract: We prove that witnessed symmetric choice strictly increases the expressive power of choiceless polynomial time with counting. A fixed sentence with one witnessed-choice occurrence defines a Boolean query on every finite input that is not definable in the original 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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