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Anderson's Quasi-Completeness Question

Algebra · posed by D. D. Anderson, 2014 · disproved

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Statement

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.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. construction · #1

    Rethlas + Archon (GPT-5.4 Pro)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    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.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

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

    Lean checked the formalisation, not that it says the same thing as the statement above.

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