What was already known
Stable uniformity was known to imply sheafiness. Earlier uniform examples with bad localizations or failed sheafiness did not give these uniform, sheafy counterexamples.
AI involvement
The paper credits ChatGPT 5.6 Sol with both main results. Birkbeck and Torzewski framed and coauthored the work; Claude Fable 5 formalized it.
The paper credits ChatGPT 5.6 Sol with both counterexample results, while the named human authors framed and presented the work; Claude's code production is separate from discovery.
Importance
Separates strong sheafiness from stable uniformity through two explicit constructions.
Limitations
The formal check covers finite-jet endpoints and the weighted-parity example at weight w(n)=n, sufficient for the existential answer. It does not cover the paper’s claim for every unbounded weight. Human mathematical sign-off was still pending in the reviewed record. The companion paper was read on a moving branch, so its exact revision at the formal record’s date is uncertain.
Technical verification
The cited record reports Lean kernel and Comparator certification of the finite-jet conclusions and weighted-parity endpoints with standard axioms. The finite-jet Palomar surface uses the restricted Laurent-series base, with additional abstract-base endpoints in the library; the weighted-parity check covers w(n)=n. These exact certified instances suffice for the existential negative answer, while the broader paper scope is not fully covered by the selected comparison.
Independent checking
Kernel replay, challenge/solution statement comparison and standard-axiom checks; bridge identifies public and library definitions
- Checker
- Lean kernel and Comparator in Birkbeck and Torzewski's pinned repository
- Scope
- Finite-jet sheafiness, uniformity and failure of stable uniformity, plus weighted-parity sheafiness and failure of stable uniformity at w(n)=n
- Basis
- Reported by the linked checker
Human understanding
Default for missing evidence of independent human understanding: the authors' paper explains the constructions, but it was AI-assisted and the cited record documents only AI review, with human mathematical sign-off pending.
Correction and publication history
Separates strong sheafiness from stable uniformity through two explicit constructions.
Read this published revision