Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 141-01. Existential–universal real sentences in the counting hierarchy
Manuscript map · lines 5155–5164
OpenAI@2026-10-07#rem:oai-p-141-01
Authors: OpenAI. Family 141.
Title: Existential–universal real sentences in the counting hierarchy.
Abstract: We prove that the existential theory of the reals lies in the counting hierarchy. More generally, we show that the truth of existential–universal sentences over the reals can be decided in a fixed level of the counting hierarchy, even when the integer polynomials are given by arithmetic circuits.
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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