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Explicit Presentation of the 2-adic Absolute Galois Group

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two-adic-absolute-galois-presentationAlgebraposed by 1982recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

Give an explicit profinite presentation of Gal(Q2/Q2)\operatorname{Gal}(\overline{\mathbb{Q}}_2 / \mathbb{Q}_2). The tame local cases were settled by the early 1980s; the dyadic case was the last one missing. The new presentation has four generators, two word relations and a pro-22 condition on the wild generators.

Context

The p=2 gap left by Jannsen-Wingberg (1982), a known hole in Galois theory.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionChatGPT-5.5 Pro (GPT-5.6 A/B), Claude Fable 5, Claude Opus 4.8 with David Roe, David Turturean ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    ChatGPT-5.5 Pro (GPT-5.6 A, B), Claude Fable 5, Claude Opus 4.8
    people
    David Roe, David Turturean

    A ChatGPT Pro conversation produced the candidate presentation with an informal proof; it passed Roe's finite-quotient verifier on all 5,402 test groups, and the proof was then formalized twice in Lean 4 with coding agents.

    Reviews

    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      Two separately initiated Lean 4 formalizations, checked modulo 7 and 9 named interfaces to the classical literature respectively. Manuscript public with an interactive web edition; not yet externally peer-reviewed.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Endorsements

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    Discussion of this attempt

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