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We say that $G$ \\emph{synchronizes} $f$ if the transformation semigroup $\\langle G,f\\rangle$ contains a constant map, and that $G$ is a \\emph{synchronizing group} if $G$ synchronizes \\emph{every} non-permutation.\n  A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every non-synchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has pa"},"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":"1504.01629","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-07T14:59:30Z","cross_cats_sorted":[],"title_canon_sha256":"1e15c8306ddd6e72bc9157e041cb84c5e70860ad88b77aac7fcb54492c8d998a","abstract_canon_sha256":"cfdd1d10d418d426fbac1c6dd4754afb98fd1688f8247e1e7681c650d9d637fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:59.708613Z","signature_b64":"jlDUzqdBbfH3ItwYcQRh2cyKROps9lfQx+VLOjd7CKVNR86gheC0mAqhz7vE6U/l8uWIJGRQ5yyc3V5WFlDoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"407989f9b60bcc85c0de6e7adc3a499a6269c48ec93c6a8a3d571f55559edac1","last_reissued_at":"2026-05-18T00:15:59.708215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:59.708215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Primitive groups and synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Artur Schaefer, Gordon Royle, Jo\\~ao Ara\\'ujo, Peter J. 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