Not evaluated
The Courtade–Kumar and Hellinger conjectures (family 119)
The gist
On October 6, 2026, OpenAI released two manuscripts on the Courtade–Kumar and Hellinger conjectures.
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-119-courtadekumar-hellinger-conjectures-r1
@misc{discoveria-oai-fam-119-courtadekumar-hellinger-conjectures-r1,
author = {{DiscoverIA}},
title = {The Courtade–Kumar and Hellinger conjectures (family 119)},
howpublished = {DiscoverIA registry, entry oai-fam-119-courtadekumar-hellinger-conjectures},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-119-courtadekumar-hellinger-conjectures#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 manuscripts held, they would bring results on information contraction, that is, on how much of a signal survives noise. The first deals with a “sharp” (announced as optimal) contraction of binary information on the discrete cube, the set of strings of zeros and ones of a given length. The second deals with Hellinger contraction (a gap between two probability distributions) for arbitrary Boolean output bias: the output, with two values, need not be balanced.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and the repository marks its review “unchecked”. No third-party verification is recorded. The manuscripts come from an internal model that OpenAI has not released.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 119.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 · Sharp-binary-information…link only, reading not recorded
- Repositorygithub.com · Hellinger-contraction…link only, reading not recorded
- Lean proofgithub.com · 119.mdpage read word for word
- Lean proofgithub.com · CourtadeKumar.leanlink only, reading not recorded
- Lean proofgithub.com · SoftChannel204.leanlink only, reading not recorded
Method
In the openai/math release, family 119 has two manuscripts dated September 24, 2026, filed under the section “Theoretical computer science” of overview.tex. They are “Sharp binary-information contraction on the discrete cube” and “Hellinger contraction with arbitrary Boolean output bias”; history.md reports no revision. OpenAI adds 2 Lean Comparator files, lean/ComparatorChallenges/CourtadeKumar.lean and lean/ComparatorChallenges/SoftChannel204.lean, described in lean/docs/119.md. 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 119, section “Theoretical computer science”, 2 manuscripts dated Sep 24, 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
- 6 : 1 read word for word, 5 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 116 of 372, by family number
- Not evaluated : Uniform identity testing for noncommutative formulas (family 116)
- Not evaluated : Uniform sparsest cut: hardness and semidefinite gaps (family 117)
- Not evaluated : Unbounded bin-packing gaps and the modified integer round-up conjecture (family 118)
- Not evaluated : The Courtade–Kumar and Hellinger conjectures (family 119)
- Not evaluated : Almost-linear-time exact matching in general graphs (family 120)
- Not evaluated : Almost-linear expected-time approximation of edit distance (family 121)
- Not evaluated : Superpolynomial lower bounds and quasipolynomial reconstruction from deletion traces (family 122)
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