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A point $G$ in $\\mathcal{A}$ is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at $G$ is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is"},"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":"1611.01633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-05T11:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"d7cb42cc01bbc844bb10d146b33363c9bf0fc2b4434b0e82a31f31d592d46a1b","abstract_canon_sha256":"b700213cae57d896dba3b94e29883bc95d12f7d29e53cdefc7d9b14a370848e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:04.813402Z","signature_b64":"W1D3NoC1i81EdsQvN9gfAlhv1YsgMwvWeDRPSzICLpzP6yAC8za8bikAt4TDKVhprtCf6GKBVP3uZQWFi0EkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da7e481e7db615b0e808aae60a2487b4bf5a91821170f7ec2d633a06acfb6dac","last_reissued_at":"2026-05-18T01:00:04.812873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:04.812873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of centralizers and derivations on some algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jiankui Li, Jun He, Wenhua Qian","submitted_at":"2016-11-05T11:28:09Z","abstract_excerpt":"A linear mapping $\\phi$ on an algebra $\\mathcal{A}$ is called a centralizable mapping at $G\\in\\mathcal{A}$ if $\\phi(AB)=\\phi(A)B=A\\phi(B)$ for each $A$ and $B$ in $\\mathcal{A}$ with $AB=G$, and $\\phi$ is called a derivable mapping at $G\\in\\mathcal{A}$ if $\\phi(AB)=\\phi(A)B+A\\phi(B)$ for each $A$ and $B$ in $\\mathcal{A}$ with $AB=G$. A point $G$ in $\\mathcal{A}$ is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at $G$ is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01633","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":"1611.01633","created_at":"2026-05-18T01:00:04.812964+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01633v1","created_at":"2026-05-18T01:00:04.812964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01633","created_at":"2026-05-18T01:00:04.812964+00:00"},{"alias_kind":"pith_short_12","alias_value":"3J7EQHT5WYK3","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3J7EQHT5WYK3B2AI","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3J7EQHT5","created_at":"2026-05-18T12:29:55.572404+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/3J7EQHT5WYK3B2AIVLTAUJEHWS","json":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS.json","graph_json":"https://pith.science/api/pith-number/3J7EQHT5WYK3B2AIVLTAUJEHWS/graph.json","events_json":"https://pith.science/api/pith-number/3J7EQHT5WYK3B2AIVLTAUJEHWS/events.json","paper":"https://pith.science/paper/3J7EQHT5"},"agent_actions":{"view_html":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS","download_json":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS.json","view_paper":"https://pith.science/paper/3J7EQHT5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01633&json=true","fetch_graph":"https://pith.science/api/pith-number/3J7EQHT5WYK3B2AIVLTAUJEHWS/graph.json","fetch_events":"https://pith.science/api/pith-number/3J7EQHT5WYK3B2AIVLTAUJEHWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS/action/storage_attestation","attest_author":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS/action/author_attestation","sign_citation":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS/action/citation_signature","submit_replication":"https://pith.science/pith/3J7EQHT5WYK3B2AIVLTAUJEHWS/action/replication_record"}},"created_at":"2026-05-18T01:00:04.812964+00:00","updated_at":"2026-05-18T01:00:04.812964+00:00"}