Not evaluated
Finite lattice representation: counterexamples and undecidability (family 206)
The gist
OpenAI claims, on October 6, 2026, characterisation and undecidability results on finite congruence lattices, and a negative solution to their representation problem.
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-206-finite-lattice-representation-r1
@misc{discoveria-oai-fam-206-finite-lattice-representation-r1,
author = {{DiscoverIA}},
title = {Finite lattice representation: counterexamples and undecidability (family 206)},
howpublished = {DiscoverIA registry, entry oai-fam-206-finite-lattice-representation},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-206-finite-lattice-representation#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The finite lattice representation problem asks whether every finite lattice can be seen as the congruence lattice of a finite algebra. A congruence lattice is the structure formed by the ways of grouping the elements of the algebra into classes compatible with its operations. If the manuscript “A negative solution to the finite lattice representation problem” held, the answer would be no: some finite lattices would be realised by no finite algebra.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by the claimant and marked “review: status: unchecked” in formalization.yaml. No third-party check has been read. It is not known what the undecidability result would state exactly, nor which of the two manuscripts the Lean covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 206.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 · Finite-Congruence…link only, reading not recorded
- Repositorygithub.com · A-Negative-Solution-to…link only, reading not recorded
- Lean proofgithub.com · 206.mdpage read word for word
- Lean proofgithub.com · FiniteCongruenceGraph.leanlink only, reading not recorded
Method
Two manuscripts, dated September 24, 2026: “Finite congruence lattices: characterization and undecidability” and “A negative solution to the finite lattice representation problem”. A Comparator statement is described in lean/docs/206.md, with the file lean/ComparatorChallenges/FiniteCongruenceGraph.lean. The family is absent from the `sources` of formalization.yaml; 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: “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 (Algebra)
- In openai/math
- family 206, section “Algebra”, 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
- 5 : 1 read word for word, 4 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 200 of 372, by family number
- Not evaluated : Donovan's conjecture over fields and discrete valuation rings (family 203)
- Not evaluated : Tensor saturation for even spin groups (family 204)
- Not evaluated : Saxl's conjecture and universal tensor squares (family 205)
- Not evaluated : Finite lattice representation: counterexamples and undecidability (family 206)
- Not evaluated : The ℓ¹-Bass and complex Bass trace conjectures (family 207)
- Not evaluated : The finite Benson–Etingof–Ostrik conjecture (family 208)
- Not evaluated : Integral counterexamples to Gersten’s conjecture (family 209)
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