Not evaluated
The Shareshian–Wachs e-positivity conjecture (family 169)
The gist
On October 6, 2026, OpenAI announced a manuscript on the elementary positivity of chromatic quasisymmetric functions, from an unreleased internal model.
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.
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript were correct, it would bring, according to its title, an elementary positivity (e-positivity) result for chromatic quasisymmetric functions. A function is e-positive when it decomposes into elementary symmetric functions with non-negative coefficients. A chromatic quasisymmetric function is an algebraic object attached to a graph, which encodes its colourings where two neighbouring vertices have different colours.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file formalization.yaml marks it “unchecked”. No third-party verification is recorded, and the sources read do not say which graphs the claimed result applies to.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 169.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 · Elementary-Positivity-of…link only, reading not recorded
- Lean proofgithub.com · 169.mdpage read word for word
- Lean proofgithub.com · ElementaryPositivity.leanlink only, reading not recorded
Method
The openai/math repository contains one manuscript, “Elementary positivity of chromatic quasisymmetric functions”, dated September 24, 2026 and filed under the section “Combinatorics” (overview.tex). The file lean/docs/169.md describes the scope of the Lean formalisation, with 1 Comparator statement (lean/ComparatorChallenges/ElementaryPositivity.lean). In formalization.yaml, the family is not among the listed sources; 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
- Mathematics (Combinatorics)
- In openai/math
- family 169, section “Combinatorics”, 1 manuscript 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
- 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 163 of 372, by family number
- Not evaluated : The higher-dimensional Erdős distinct-distances conjecture (family 166)
- Not evaluated : Pinned distances and a power saving for planar unit distances (family 167)
- Not evaluated : Combinatorial invariance of Kazhdan–Lusztig polynomials (family 168)
- Not evaluated : The Shareshian–Wachs e-positivity conjecture (family 169)
- Not evaluated : Sharp logarithmic exponents for off-diagonal Ramsey numbers (family 170)
- Not evaluated : The hypercube Ramsey conjecture (family 171)
- Not evaluated : Classification of finite Euclidean Ramsey configurations (family 172)
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