{"id":"palomar/PALOMAR-2026-08-31-000008","url":"https://github.com/yoshito-ishiki-math/lean-scottish-book-155/tree/233eff4af7901eadee7927a1eb1f814ad0f3c118","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-31-000008-v1.json","repo":"https://github.com/yoshito-ishiki-math/lean-scottish-book-155","tags":["math.FA","math.MG","msc:46B20","msc:54E40","functional-analysis","banach-spaces","lean-formalization"],"score":0,"title":"yoshito-ishiki-math/lean-scottish-book-155","trust":"high","domain":"math.FA","source":"palomar","authors":["Yoshito Ishiki"],"reviews":0,"subject":"math.FA","summary":"A Lean proof that there are real Banach spaces X and Y and a bijection U from X to Y which preserves every pairwise distance on every closed ball of radius one quarter while failing to be a global isometry. This gives a counterexample to Scottish Book Problem 155.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-31","reactions":{},"formalized":true,"formalizes":[{"title":"AI-Assisted Research Report: A counterexample to Scottish Book Problem 155","identifier":"doi:10.5281/zenodo.22168214","relationship":"formalizes"}]}