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We show that the 1-skeleton of an affine Bruhat-Tits building of type $\\widetilde A_{d-1}$ is local-to-global rigid if and only if the underlying field has characteristic 0. For example the Bruhat-Tits building of $SL(d,F_p((t)))$ is not local-to-global rigid, while the Bruhat-Tits building of $SL(d,Q_p)$ is local-to-global rigid."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.02775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-09T07:42:15Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"47be224821c8b834a9834b5732ac51b2a59f3fd1b1f51dd10779f615cb6d8a5b","abstract_canon_sha256":"383216df56287c14b9caef6677241effb73f64be5e8c8f7010c797d49863139f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:44.256797Z","signature_b64":"M9Yj7xEMtIs6kuL8NEjS5F+u/4Pf6k10pQFqXDX+4OvIxGdYv/Y2b+jL17fY4Uxw4qUUkK6UtHpYNUnQPx+JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e7c432caaa4e9d9552bcc7500e8da08e82971615e464886f1ea9ca7dc66353","last_reissued_at":"2026-05-18T00:33:44.256201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:44.256201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local-to-global rigidity of Bruhat-Tits buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Mikael de la Salle, Romain Tessera","submitted_at":"2015-12-09T07:42:15Z","abstract_excerpt":"A vertex-transitive graph X is called local-to-global rigid if there exists R such that every other graph whose balls of radius R are isometric to the balls of radius R in X is covered by X. Let $d\\geq 4$. We show that the 1-skeleton of an affine Bruhat-Tits building of type $\\widetilde A_{d-1}$ is local-to-global rigid if and only if the underlying field has characteristic 0. 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