Not evaluated
Counterexamples to Baum–Connes and Kadison–Kaplansky (family 285)
The gist
On October 6, 2026, OpenAI announced three manuscripts on counterexamples: two for Baum–Connes in its reduced form, one for the Kadison–Kaplansky projection conjecture.
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-285-counterexamples-baumconnes-kadisonkaplansky-r1
@misc{discoveria-oai-fam-285-counterexamples-baumconnes-kadisonkaplansky-r1,
author = {{DiscoverIA}},
title = {Counterexamples to Baum–Connes and Kadison–Kaplansky (family 285)},
howpublished = {DiscoverIA registry, entry oai-fam-285-counterexamples-baumconnes-kadisonkaplansky},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-285-counterexamples-baumconnes-kadisonkaplansky#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The Kadison–Kaplansky projection conjecture concerns torsion-free groups (groups with no element of finite order other than the identity). If the manuscripts were correct, these statements, in the forms their titles target, would be false.
What remains unclear
No third-party assessment has been found, and no Lean (a language in which a computer checks every step of a proof) is supplied. The sources read do not give the precise statements of the counterexamples.
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 · …Reduced-Baum-Connes…link only, reading not recorded
- Repositorygithub.com · …the-Kadison-Kaplansky…link only, reading not recorded
- Repositorygithub.com · An-Irrational-Trace…link only, reading not recorded
Method
Three manuscripts, all dated September 23, 2026. The first is titled “A torsion-free counterexample to reduced Baum–Connes injectivity”. The second is titled “An irrational-trace counterexample to reduced Baum–Connes”. The third is titled “A torsion-free counterexample to the Kadison–Kaplansky projection conjecture”. The section of overview.tex for family 285 is “Operator algebras”, and history.md reports no revision. 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 (Operator algebras)
- In openai/math
- family 285, section “Operator algebras”, 3 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 4 : 4 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 279 of 372, by family number
- Not evaluated : Scale-to-conformal enhancement in four-dimensional QFT (family 282)
- Not evaluated : Polynomial-time, constant-error unitary synthesis from a Boolean oracle (family 283)
- Not evaluated : The optimal randomized–quantum query exponent (family 284)
- Not evaluated : Counterexamples to Baum–Connes and Kadison–Kaplansky (family 285)
- Not evaluated : Arithmetic rigidity of lattice von Neumann algebras (family 286)
- Not evaluated : Isomorphism of free group factors (family 287)
- Not evaluated : Kadison's similarity conjecture (family 288)
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