Not evaluated
The existential theory of the reals and existential–universal sentences in the counting hierarchy (family 141)
The gist
In its release of October 6, 2026, OpenAI presents, using an unreleased internal model, a manuscript on existential–universal real sentences in the counting hierarchy.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-141-existential-theory-reals-r1
@misc{discoveria-oai-fam-141-existential-theory-reals-r1,
author = {{DiscoverIA}},
title = {The existential theory of the reals and existential–universal sentences in the counting hierarchy (family 141)},
howpublished = {DiscoverIA registry, entry oai-fam-141-existential-theory-reals},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-141-existential-theory-reals#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The counting hierarchy is a family of complexity classes (categories of problems according to the computing resources they require). If the manuscript held, it would bring a result on statements about the real numbers that begin with a “there exists” and continue with a “for all”, within this hierarchy.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party evaluation is recorded. The sources read give only the manuscript's title, not its statement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Existential-universal…link only, reading not recorded
Method
The openai/math repository contains the manuscript “Existential–universal real sentences in the counting hierarchy”, dated October 4, 2026. The family has no lean/docs/141.md file; history.md reports no revision of this manuscript. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Theoretical computer science
- In openai/math
- family 141, section “Theoretical computer science”, 1 manuscript dated Oct 4, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 137 of 372, by family number
- Not evaluated : Subset Sum in O(2^(0.49n)) time (family 138)
- Not evaluated : Subpolynomial queries for log-concave sampling (family 139)
- Not evaluated : Memory–sample lower bounds for noiseless Gaussian regression (family 140)
- Not evaluated : The existential theory of the reals and existential–universal sentences in the counting hierarchy (family 141)
- Not evaluated : Deterministic polynomial factorization over prime fields (family 142)
- Not evaluated : Uniform limit-cycle bounds in Hilbert's sixteenth problem (family 143)
- Not evaluated : Banach's simple Lebesgue-spectrum problem (family 144)
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