{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QIBM6MVKEKOCK4J3SNDWRP42V3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"02a46aecbe5b1abf714125855c5f2be4b495f2878e383bfaa7db6832a728f00f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T10:22:31Z","title_canon_sha256":"da1c75b9065c5e91cc8883daf35e6194de14e3aa2be8878fbaeb299488188e6d"},"schema_version":"1.0","source":{"id":"1411.4795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4795","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4795v2","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4795","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"pith_short_12","alias_value":"QIBM6MVKEKOC","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QIBM6MVKEKOCK4J3","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QIBM6MVK","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f40218c5076a72cd63f64530a07de28605ecd815ff4ad8c601622fb7171d2c91","target":"graph","created_at":"2026-05-18T02:32:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that every weak-local derivation on a C$^*$-algebra is continuous, and the same conclusion remains valid for weak$^*$-local derivations on von Neumann algebras. We further show that weak-local derivations on C$^*$-algebras and weak$^*$-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal $^*$-automorphism with our notions of extreme-strong-local derivations and automorphisms.","authors_text":"Ahlem Ben Ali Essaleh, Antonio M. Peralta, Mar\\'Ia Isabel Ram\\'Irez","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T10:22:31Z","title":"Weak-local derivations and homomorphisms on C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4795","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:07e2636f31b4bdf737e6396a5b1138e4de4a088e4543ae8189d356737db1ab6b","target":"record","created_at":"2026-05-18T02:32:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"02a46aecbe5b1abf714125855c5f2be4b495f2878e383bfaa7db6832a728f00f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T10:22:31Z","title_canon_sha256":"da1c75b9065c5e91cc8883daf35e6194de14e3aa2be8878fbaeb299488188e6d"},"schema_version":"1.0","source":{"id":"1411.4795","kind":"arxiv","version":2}},"canonical_sha256":"8202cf32aa229c25713b934768bf9aaee9e6c0ce32955ac62a8c63b64efcb8a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8202cf32aa229c25713b934768bf9aaee9e6c0ce32955ac62a8c63b64efcb8a3","first_computed_at":"2026-05-18T02:32:38.200795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:38.200795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2vCrpNPRWln6o4z+FD0jk1S84qUANtYhcvX/mwJ2m6Og58jHOwEp+ld2q6RvUMPtkmkB5l/kPUfabb7FSoVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:38.201169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07e2636f31b4bdf737e6396a5b1138e4de4a088e4543ae8189d356737db1ab6b","sha256:f40218c5076a72cd63f64530a07de28605ecd815ff4ad8c601622fb7171d2c91"],"state_sha256":"0bfd2303e8a5b226b99e2f22e098a4390af2fea0414ca600190b78ba3dba3337"}