Not evaluated
Beyond the square-root exponent for depth-three circuits (family 112)
The gist
In its release of October 6, 2026, OpenAI claims, in a manuscript, a result beyond the square-root exponent for depth-three Boolean circuits.
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-112-beyond-square-root-exponent-depth-three-r1
@misc{discoveria-oai-fam-112-beyond-square-root-exponent-depth-three-r1,
author = {{DiscoverIA}},
title = {Beyond the square-root exponent for depth-three circuits (family 112)},
howpublished = {DiscoverIA registry, entry oai-fam-112-beyond-square-root-exponent-depth-three},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-112-beyond-square-root-exponent-depth-three#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If this result held, it would concern Boolean circuits (networks of logic gates) of depth three, an object of theoretical computer science. An exponent describes how a quantity grows with the problem size: a “square-root” exponent corresponds to the power one half.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: no third-party check is recorded, and formalization.yaml carries the mention “unchecked”. It is not known whether the Lean statement faithfully matches the manuscript's. The sources read do not say what quantity the exponent measures.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 112.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 · Beyond-the-Square-Root…link only, reading not recorded
- Lean proofgithub.com · 112.mdpage read word for word
- Lean proofgithub.com · DepthThree.leanlink only, reading not recorded
Method
The openai/math repository holds the manuscript “Beyond the Square-Root Exponent for Depth-Three Boolean Circuits”, dated September 23, 2026. It also holds the Lean file lean/ComparatorChallenges/DepthThree.lean. The page lean/docs/112.md describes the scope of the Lean formalisation and lists 1 Comparator statement; 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Theoretical computer science
- In openai/math
- family 112, section “Theoretical computer science”, 1 manuscript dated Sep 23, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 109 of 372, by family number
- Not evaluated : Integer multiplication below n log n (family 109)
- Not evaluated : Optimal-order randomized k-server on arbitrary metrics (family 110)
- Not evaluated : One-sample matroid prophet inequalities against an almighty adversary (family 111)
- Not evaluated : Beyond the square-root exponent for depth-three circuits (family 112)
- Not evaluated : Approximate counting and the perfect-matching entropy conjecture (family 113)
- Not evaluated : Approximate counting of common integer polymatroid bases (family 114)
- Not evaluated : Sampling and counting contingency tables with arbitrary margins (family 115)
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