Explicit Presentation of the 2-adic Absolute Galois Group
Give an explicit profinite presentation of . 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- condition on the wild generators.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Algebraic number theory
- Posed by
- —
- Year posed
- 1982
- Years open
- 44y
- Solved
- 2026-07-26
- Model
- ChatGPT-5.5 Pro (GPT-5.6 A/B), Claude Fable 5, Claude Opus 4.8
- Vendor
- OpenAI / Anthropic
- Collaborators
- David Roe, David Turturean
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.
Verification
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.
Sources
A presentation of the absolute Galois group of Q2 (project site)