What was already known
Explicit presentations were known for odd primes. Earlier work established finite presentability and abstract generator and relation counts for Q₂, but no explicit marked presentation.
AI involvement
Turturean directed the search; GPT-5.5 Pro generated the corrected relation and proof manuscript. Roe checked finite quotients and reportedly read the proof; Roe and Turturean developed Lean formalizations and refined the manuscript.
The development account attributes the retained corrected relation and original proof manuscript to GPT, with substantive human problem direction and later verification.
Importance
Provides the previously missing explicit dyadic presentation for local Galois calculations.
Limitations
The two reported Lean proofs rely on identified literature inputs, and one adapted four steps from the other. Agreement on 5,402 finite groups supports the candidate but does not prove the profinite presentation; the manuscript is not externally peer reviewed.
Technical verification
The project reports Lean 4 proofs of the marked presentation in two separately initiated projects, conditional on nine and seven identified literature inputs respectively. Roe's theorem and comparator target are explicitly the paper's marked presentation; finite-quotient agreement for 5,402 groups is supporting evidence, not the proof. A human read of the natural-language proof is also reported. No local Lean rebuild was done here.
Formal checking
Two separately initiated sorry-free formalizations and comparator targets
- Checker
- Roe and Turturean's Lean 4 developments
- Scope
- The marked profinite presentation of G_Q2 in Theorem 1.2
- Basis
- Reported by the linked checker
Formal checking
Read the manuscript and confirmed its proof after running the finite-quotient verifier, as reported by Turturean
- Checker
- David Roe
- Scope
- The candidate presentation and natural-language proof in the preserved manuscript
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Roe and Turturean explain the finite-quotient strategy, marked tame/pro-2 comparisons, lifting counts and reconstruction in the paper and project account. Full concerns the presentation argument; it does not imply every external input is newly explained or formalized.
Correction and publication history
Provides the previously missing explicit dyadic presentation for local Galois calculations.
Read this published revision