Not evaluated
Chromatic splitting: counterexamples and filtrations (family 318)
The gist
In its release of October 6, 2026, OpenAI presents five manuscripts on chromatic splitting, with counterexamples and filtrations.
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-318-chromatic-splitting-counterexamples-r1
@misc{discoveria-oai-fam-318-chromatic-splitting-counterexamples-r1,
author = {{DiscoverIA}},
title = {Chromatic splitting: counterexamples and filtrations (family 318)},
howpublished = {DiscoverIA registry, entry oai-fam-318-chromatic-splitting-counterexamples},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-318-chromatic-splitting-counterexamples#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscripts were correct, one would provide counterexamples to “weak” chromatic splitting and another a rational obstruction to its “strong” version at height three. Other manuscripts would concern the failure of “finite assembly” for a chromatic overlap at the prime three, and filtrations.
What remains unclear
No proof in Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party verification is recorded. The five manuscripts do not have the same subject, and the sources read do not give their exact statements.
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 · Filtered-chromatic…link only, reading not recorded
- Repositorygithub.com · The-height-three…link only, reading not recorded
- Repositorygithub.com · A-rational-obstruction-to…link only, reading not recorded
- Repositorygithub.com · Failure-of-finite…link only, reading not recorded
- Repositorygithub.com · Counterexamples-to-weak…link only, reading not recorded
Method
The openai/math repository contains five manuscripts dated September 25 and 27, 2026, including “Counterexamples to weak chromatic splitting: sphere kernels and descent exponents”. No lean/docs/318.md file is supplied; history.md reports no revision of these manuscripts. 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
- Mathematics (Topology)
- In openai/math
- family 318, section “Topology”, 5 manuscripts dated Sep 25, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 6 : 6 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 312 of 372, by family number
- Not evaluated : The four-dimensional Singer conjecture (family 315)
- Not evaluated : Curtis’s conjecture (family 316)
- Not evaluated : Thomason model structures in every strict higher dimension (family 317)
- Not evaluated : Chromatic splitting: counterexamples and filtrations (family 318)
- Not evaluated : Counterexamples to the Hahn–Wilson conjecture at height two (family 319)
- Not evaluated : A four-dimensional counterexample to Borel rigidity (family 320)
- Not evaluated : A counterexample to Wall's finite D(2) conjecture (family 321)
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