Not evaluated
Subpolynomial queries for log-concave sampling (family 139)
The gist
In its release of October 6, 2026, OpenAI claims subpolynomial query complexity for sampling from well-conditioned log-concave distributions.
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-139-subpolynomial-queries-log-concave-sampling-r1
@misc{discoveria-oai-fam-139-subpolynomial-queries-log-concave-sampling-r1,
author = {{DiscoverIA}},
title = {Subpolynomial queries for log-concave sampling (family 139)},
howpublished = {DiscoverIA registry, entry oai-fam-139-subpolynomial-queries-log-concave-sampling},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-139-subpolynomial-queries-log-concave-sampling#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 the manuscript held, the number of queries would be subpolynomial: bounded by a quantity that grows more slowly than any positive power of a size parameter that the sources read do not specify. A query is a consultation of the distribution; sampling means drawing random points according to it. A distribution is log-concave when the logarithm of its density is concave, dome-shaped; “well-conditioned” denotes a technical regularity condition that the sources read do not detail.
What remains unclear
No independent assessment is recorded. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI and marked “review: status: unchecked” in formalization.yaml.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 139.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 · Subpolynomial-query…link only, reading not recorded
- Lean proofgithub.com · 139.mdpage read word for word
- Lean proofgithub.com · LogConcaveQuery.leanlink only, reading not recorded
Method
OpenAI publishes one manuscript, “Subpolynomial query complexity for well-conditioned log-concave sampling”, dated September 26, 2026. The repository also holds lean/docs/139.md, which describes the scope of the Lean formalisation (1 Comparator statement), and lean/ComparatorChallenges/LogConcaveQuery.lean. 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 139, section “Theoretical computer science”, 1 manuscript dated Sep 26, 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 135 of 372, by family number
- Not evaluated : The quasilinear PCP-for-PPAD conjecture (family 136)
- Not evaluated : One-tape time simulation in two-fifths-power space (family 137)
- 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)
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