{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HFEDCOT6BT53P3AOQLTJFCAKXH","short_pith_number":"pith:HFEDCOT6","schema_version":"1.0","canonical_sha256":"3948313a7e0cfbb7ec0e82e692880ab9ca3b05f782cd9d946bf9d0e6ce0f1adc","source":{"kind":"arxiv","id":"1605.05656","version":1},"attestation_state":"computed","paper":{"title":"Stability of derivations under weak-2-local continuous perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Enrique Jord\\'a","submitted_at":"2016-05-18T16:56:17Z","abstract_excerpt":"Let $\\Omega$ be a compact Hausdorff space and let $A$ be a C$^*$-algebra. We prove that if every weak-2-local derivation on $A$ is a linear derivation and every derivation on $C(\\Omega,A)$ is inner, then every weak-2-local derivation $\\Delta:C(\\Omega,A)\\to C(\\Omega,A)$ is a {\\rm(}linear{\\rm)} derivation. As a consequence we derive that, for every complex Hilbert space $H$, every weak-2-local derivation $\\Delta : C(\\Omega,B(H)) \\to C(\\Omega,B(H))$ is a (linear) derivation. We actually show that the same conclusion remains true when $B(H)$ is replaced with an atomic von Neumann algebra. With a m"},"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":"1605.05656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-18T16:56:17Z","cross_cats_sorted":[],"title_canon_sha256":"b42add4d83108ef22ff9b71aff8d725cb92d413a0d952fb67c39cce35a98f308","abstract_canon_sha256":"72c9d2d26189fff0becf3656414f0384ae84c28bcbce5014e0d279eea11eddfd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:30.115296Z","signature_b64":"L2HUjmtc5cGS9ObVTK6DUgplLlb4csnLUSVmugF10jwfm3CslDrprDMyadTICItRCWW4IEczn5/y1iAcSyBhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3948313a7e0cfbb7ec0e82e692880ab9ca3b05f782cd9d946bf9d0e6ce0f1adc","last_reissued_at":"2026-05-18T01:14:30.114850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:30.114850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of derivations under weak-2-local continuous perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Enrique Jord\\'a","submitted_at":"2016-05-18T16:56:17Z","abstract_excerpt":"Let $\\Omega$ be a compact Hausdorff space and let $A$ be a C$^*$-algebra. We prove that if every weak-2-local derivation on $A$ is a linear derivation and every derivation on $C(\\Omega,A)$ is inner, then every weak-2-local derivation $\\Delta:C(\\Omega,A)\\to C(\\Omega,A)$ is a {\\rm(}linear{\\rm)} derivation. As a consequence we derive that, for every complex Hilbert space $H$, every weak-2-local derivation $\\Delta : C(\\Omega,B(H)) \\to C(\\Omega,B(H))$ is a (linear) derivation. We actually show that the same conclusion remains true when $B(H)$ is replaced with an atomic von Neumann algebra. With a m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05656","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.05656","created_at":"2026-05-18T01:14:30.114921+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05656v1","created_at":"2026-05-18T01:14:30.114921+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05656","created_at":"2026-05-18T01:14:30.114921+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFEDCOT6BT53","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFEDCOT6BT53P3AO","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFEDCOT6","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH","json":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH.json","graph_json":"https://pith.science/api/pith-number/HFEDCOT6BT53P3AOQLTJFCAKXH/graph.json","events_json":"https://pith.science/api/pith-number/HFEDCOT6BT53P3AOQLTJFCAKXH/events.json","paper":"https://pith.science/paper/HFEDCOT6"},"agent_actions":{"view_html":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH","download_json":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH.json","view_paper":"https://pith.science/paper/HFEDCOT6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05656&json=true","fetch_graph":"https://pith.science/api/pith-number/HFEDCOT6BT53P3AOQLTJFCAKXH/graph.json","fetch_events":"https://pith.science/api/pith-number/HFEDCOT6BT53P3AOQLTJFCAKXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH/action/storage_attestation","attest_author":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH/action/author_attestation","sign_citation":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH/action/citation_signature","submit_replication":"https://pith.science/pith/HFEDCOT6BT53P3AOQLTJFCAKXH/action/replication_record"}},"created_at":"2026-05-18T01:14:30.114921+00:00","updated_at":"2026-05-18T01:14:30.114921+00:00"}