VibeMathedMath problems solved by AI
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Anderson's Quasi-Completeness Question

Is every weakly quasi-complete Noetherian local ring quasi-complete? Asked by D. D. Anderson in 2014. The ring A=kp[[X,Y]][k]A = k^p[[X, Y]][k] with k=Fp(u1,u2,… )k = \mathbb{F}_p(u_1, u_2, \dots) is weakly quasi-complete but not quasi-complete.

Result
Disproved
Status
Resolved
AI contribution
AI-discovered
Method
Construction
Field
Commutative algebra
Posed by
D. D. Anderson
Year posed
2014
Years open
12y
Solved
2026-04-04
Model
Rethlas + Archon (GPT-5.4 Pro)
Vendor
OpenAI
Collaborators
—
Verification
Lean-verified
Publication
Preprint
Significance
10 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

The dual-agent framework (Rethlas for informal reasoning, Archon for formal verification) ran roughly 80 hours; the decisive example is a classical ring going back to Nagata, which the system recognized as answering Anderson's question.

Verification

Lean-checked with a statement comparator guarding against misformalization; arXiv preprint documents the pipeline.

Source

arXiv:2604.03789 - Automated conjecture resolution with formal verification

Discussion