What was already known
Complete Noetherian local rings are quasi-complete, and quasi-complete rings are weakly quasi-complete. D. D. Anderson asked in 2014 whether the reverse implication holds for Noetherian local rings. The new construction uses earlier criteria of Anderson and Farley and Jensen’s prescribed-completion theorem.
AI involvement
The paper reports Rethlas autonomously found the Jensen-based counterexample from the posed question, while Archon autonomously formalized the complete proof; humans supplied source PDFs and later revised exposition without changing the logical argument.
Importance
Answers a named specialist question in commutative algebra by an explicit existence construction.
Limitations
The VibeMathed feed names a different specific example from the one proved in this paper. This record assesses only the existential theorem in the primary paper. The authors report human editing of exposition and a human-reviewed simplified statement;
Technical verification
The paper reports that the full Archon development builds in Lean 4 and passes Comparator against a human-reviewed existential theorem statement using standard axioms. The public challenge stub has `sorry`; the completed proof is in `Anderson/Main.lean`. This is source-reported; AIProofWatch did not reproduce the check.
Formal checking
The authors report a complete Lean 4 build and Comparator check against the human-reviewed existential statement using standard axioms. The repository distinguishes the challenge stub from the completed `Anderson/Main.lean` proof.
- Checker
- Lean 4 kernel and Comparator, as reported by the authors
- Scope
- There exists a weakly quasi-complete Noetherian local ring that is not quasi-complete.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The paper says the human authors refactored the AI proof solely for exposition, and Sections 4 and 7 explain the Jensen construction and reduction.
Correction and publication history
Primary paper, contribution attribution, prior baseline and checking scope reviewed for non-notifying local inclusion.
Read this published revision