Not evaluated
Gardam's Ã₂ lattice has no unique products: Lean proof by the author
Gardam's Ã₂ lattice has no unique products: Lean proof supplied by the author, written with intensive use of Claude
The gist
The authors of arXiv paper 2609.22380 claim, in September 2026, that Gardam's Ã2 lattice has no unique products. The proof is checked by the Lean kernel and was written with heavy use of Claude. Status: not yet evaluated.
DiscoverIA status on October 11, 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 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-gardam-a2-no-unique-products-r1
@misc{discoveria-gardam-a2-no-unique-products-r1,
author = {{DiscoverIA}},
title = {Gardam's Ã₂ lattice has no unique products: Lean proof supplied by the author, written with intensive use of Claude},
howpublished = {DiscoverIA registry, entry gardam-a2-no-unique-products},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/gardam-a2-no-unique-products#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the proof held, this lattice would be a case where the unique products property fails. The Lean kernel, which checks each step of the proof, would back this result.
What remains unclear
No third party has checked the proof, and the Lean proof has not been replayed. According to Section 10 of the paper, Claude wrote most of the Lean formalisation and of the Python program.
Read the paper
A Machine-Checked Proof that Gardam's $\tilde{A}_2$ Lattice Does Not Have Unique Products
What it establishes : Mian and Siddique exhibit two finite subsets, of 32 and 28 elements, of the group proposed by Gardam, which show that the group lacks the unique-product property; the Lean kernel checks this witness.
Where to start : The abstract, then Theorem 1.1 (Section 1), a statement due to Gardam; the authors' proof is the Lean theorem gamma_not_uniqueProds (Section 4). Section 1 says what is not formalised, Section 10 how Claude was used.
Written by an AI · reviewed by a human
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2609.22380
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 sourcearxiv.org · pdf/2609.22380page read word for word · consulted on Oct 20, 2026 ·
Claude (Anthropic), between July and September 2026
- Paperarxiv.org · abs/2609.22380page read word for word · consulted on Oct 20, 2026 ·
Use of an LLM is disclosed in Section 10.
Method
DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026; source read on October 20, 2026 from arxiv.org (page read, quotation checked word for word: “Use of an LLM is disclosed in Section 10.”).
Limits
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
- authors of arXiv 2609.22380 (Claude, July-September 2026)
announced on Sep 2026 - Nature
- new result
- Field
- Mathematics (group theory)
- Checked by
- Lean kernel; no third party
- Sources
- 2 : 2 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Authors Ibrahim Mian and Shayaan Siddique, submitted 2026-09-17 (math.GR); the Lean proof has not been re-run.
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
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