Sorries Are Not the Hard Part: An Expert-Review Case Study of a Semi-Autonomous Formalization

Large language models can often close proof gaps in interactive theorem provers, but a verified theorem is not the same thing as a reusable library contribution. We study this distinction through a detailed case study: a semi-autonomous formalization in Lean 4 of Grothendieck's vanishing theorem for sheaves of abelian groups on Noetherian topological spaces. The initial version compiles with no sorries, but an expert review found serious problems in definitions, theorem generality, file organization, and the cohomology API. We then ran a review-driven refactor and compression process and obtained a second expert review. The before-and-after comparison shows a sharp split: agents adapted well to local, mechanically checkable feedback, but remained weak at choosing definitions and designing APIs. We argue that autoformalization should be evaluated not only by closed sorries, but by whether the resulting formalization survives expert review as mathematical software.