What was already known
The assertion holds for commutative group schemes and for reduced bases; the unrestricted question had remained separate.
What changed and why it matters
Refutes a longstanding general group-scheme assertion with an explicit order-four example, retaining the known positive cases.
The AI contribution
Mathew directed Codex and Claude in the construction and formalization, takes responsibility for the contribution, and subsequently worked on understanding the example.
Limitations
This does not contradict the commutative or reduced-base theorems. Buzzard reports compiling and checking a version in July; this is attributed checking, not a AIProofWatch rerun or an audit of every later revision.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
Exact group-scheme statement and AI disclosure.
Accessible artifact / proof
Public Lean development; not recompiled by AIProofWatch.
Formal checking
Buzzard reports compilation and checking of the statement and definitions.
Checker: Kevin Buzzard
Scope: The July order-four group-scheme counterexample described in his 20 July post; no checking of subsequent revisions claimed.
Basis: Reported by the linked checker
Check date: 2026-07-20
Checking a formal statement does not establish that it matches the original problem.
Correction and publication history
Public-discussion audit found this substantive scoped contribution missing. Source statement, baseline, attribution and importance reviewed; no full proof audit. Historical addition without subscriber alerts.
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