{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IR7JAMDSJ2RNSYWNK3IEAZBZ22","short_pith_number":"pith:IR7JAMDS","canonical_record":{"source":{"id":"1205.1095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-05T03:14:43Z","cross_cats_sorted":[],"title_canon_sha256":"2ee2ac517a6c9a3b6e84613f02c09e635ee5eae0397aa7447a28c3f124b99133","abstract_canon_sha256":"93472cbae8492c3f612c1d0ab2dc2efba47f51cba406351c820153d41bc5dbcf"},"schema_version":"1.0"},"canonical_sha256":"447e9030724ea2d962cd56d0406439d6a6e0bb08b638218f7ad43130228b8b29","source":{"kind":"arxiv","id":"1205.1095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1095","created_at":"2026-05-18T03:34:59Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1095v1","created_at":"2026-05-18T03:34:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1095","created_at":"2026-05-18T03:34:59Z"},{"alias_kind":"pith_short_12","alias_value":"IR7JAMDSJ2RN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IR7JAMDSJ2RNSYWN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IR7JAMDS","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IR7JAMDSJ2RNSYWNK3IEAZBZ22","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-05T03:14:43Z","cross_cats_sorted":[],"title_canon_sha256":"2ee2ac517a6c9a3b6e84613f02c09e635ee5eae0397aa7447a28c3f124b99133","abstract_canon_sha256":"93472cbae8492c3f612c1d0ab2dc2efba47f51cba406351c820153d41bc5dbcf"},"schema_version":"1.0"},"canonical_sha256":"447e9030724ea2d962cd56d0406439d6a6e0bb08b638218f7ad43130228b8b29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:59.423086Z","signature_b64":"Qp1SrW3RQMf8xWVXqfos5VW5cBD0sPx6sw5B2KQrmfR4WlOkfJGBx0zQvCVrw4Oju5X6F7TRGLgMJWb3gGntBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"447e9030724ea2d962cd56d0406439d6a6e0bb08b638218f7ad43130228b8b29","last_reissued_at":"2026-05-18T03:34:59.422516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:59.422516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1095","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XU5UEEesBN7PNPxveQerww/ltrLDs+Bm0aGNYcGz2yZ8kFtFU5Um3bq+nrr2AvvwcUlvzV/sWCwJP0Guk5fJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:58:36.599947Z"},"content_sha256":"f14e0f389b54d19f114459bd79083a33ac0d8d41cf398a383a36eefc7c95d1d6","schema_version":"1.0","event_id":"sha256:f14e0f389b54d19f114459bd79083a33ac0d8d41cf398a383a36eefc7c95d1d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IR7JAMDSJ2RNSYWNK3IEAZBZ22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of Lie Derivations on von Neumann Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jinchuan Hou, Xiaofei Qi","submitted_at":"2012-05-05T03:14:43Z","abstract_excerpt":"Let ${\\mathcal M}$ be a von Neumann algebra without central summands of type $I_1$ and $\\xi\\in{\\mathbb C}$ a scalar. It is shown that an additive map $L$ on $\\mathcal M$ satisfies $L(AB-\\xi BA)=L(A)B-\\xi BL(A)+L(B)A-\\xi AL(B)$ whenever $A,B\\in{\\mathcal M}$ with $AB=0$ if and only if one of the following statements holds: (1) $\\xi=1$, $L=\\varphi+f$, where $\\varphi$ is an additive derivation on $\\mathcal M$ and $f$ is an additive map from $\\mathcal M$ into its center vanishing on $[A,B]$ with $AB=0$; (2)\n  $\\xi=0$, $L(I)\\in{\\mathcal Z}({\\mathcal M})$ and there exists an additive derivation $\\var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1095","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBu3wmFg4A7KLmbmUJ51NB9RUNRNm6xA9r2U5z8uCwxvEKtww3w1dyObrWRBVOd8J+n/A8q/zjaEEDggdNsYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:58:36.600356Z"},"content_sha256":"37c9cfc7b7a35c3c34052c89179b4aee449277967218c92497a59f00b1940ecd","schema_version":"1.0","event_id":"sha256:37c9cfc7b7a35c3c34052c89179b4aee449277967218c92497a59f00b1940ecd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22/bundle.json","state_url":"https://pith.science/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T22:58:36Z","links":{"resolver":"https://pith.science/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22","bundle":"https://pith.science/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22/bundle.json","state":"https://pith.science/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IR7JAMDSJ2RNSYWNK3IEAZBZ22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IR7JAMDSJ2RNSYWNK3IEAZBZ22","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":"93472cbae8492c3f612c1d0ab2dc2efba47f51cba406351c820153d41bc5dbcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-05T03:14:43Z","title_canon_sha256":"2ee2ac517a6c9a3b6e84613f02c09e635ee5eae0397aa7447a28c3f124b99133"},"schema_version":"1.0","source":{"id":"1205.1095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1095","created_at":"2026-05-18T03:34:59Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1095v1","created_at":"2026-05-18T03:34:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1095","created_at":"2026-05-18T03:34:59Z"},{"alias_kind":"pith_short_12","alias_value":"IR7JAMDSJ2RN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IR7JAMDSJ2RNSYWN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IR7JAMDS","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:37c9cfc7b7a35c3c34052c89179b4aee449277967218c92497a59f00b1940ecd","target":"graph","created_at":"2026-05-18T03:34:59Z","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":"Let ${\\mathcal M}$ be a von Neumann algebra without central summands of type $I_1$ and $\\xi\\in{\\mathbb C}$ a scalar. It is shown that an additive map $L$ on $\\mathcal M$ satisfies $L(AB-\\xi BA)=L(A)B-\\xi BL(A)+L(B)A-\\xi AL(B)$ whenever $A,B\\in{\\mathcal M}$ with $AB=0$ if and only if one of the following statements holds: (1) $\\xi=1$, $L=\\varphi+f$, where $\\varphi$ is an additive derivation on $\\mathcal M$ and $f$ is an additive map from $\\mathcal M$ into its center vanishing on $[A,B]$ with $AB=0$; (2)\n  $\\xi=0$, $L(I)\\in{\\mathcal Z}({\\mathcal M})$ and there exists an additive derivation $\\var","authors_text":"Jinchuan Hou, Xiaofei Qi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-05T03:14:43Z","title":"Characterization of Lie Derivations on von Neumann Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1095","kind":"arxiv","version":1},"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:f14e0f389b54d19f114459bd79083a33ac0d8d41cf398a383a36eefc7c95d1d6","target":"record","created_at":"2026-05-18T03:34:59Z","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":"93472cbae8492c3f612c1d0ab2dc2efba47f51cba406351c820153d41bc5dbcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-05T03:14:43Z","title_canon_sha256":"2ee2ac517a6c9a3b6e84613f02c09e635ee5eae0397aa7447a28c3f124b99133"},"schema_version":"1.0","source":{"id":"1205.1095","kind":"arxiv","version":1}},"canonical_sha256":"447e9030724ea2d962cd56d0406439d6a6e0bb08b638218f7ad43130228b8b29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"447e9030724ea2d962cd56d0406439d6a6e0bb08b638218f7ad43130228b8b29","first_computed_at":"2026-05-18T03:34:59.422516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:59.422516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qp1SrW3RQMf8xWVXqfos5VW5cBD0sPx6sw5B2KQrmfR4WlOkfJGBx0zQvCVrw4Oju5X6F7TRGLgMJWb3gGntBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:59.423086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f14e0f389b54d19f114459bd79083a33ac0d8d41cf398a383a36eefc7c95d1d6","sha256:37c9cfc7b7a35c3c34052c89179b4aee449277967218c92497a59f00b1940ecd"],"state_sha256":"065dae5004bc982c3a6bd6cdd62bd1098e46b3e777cca80e68b0563ce58b10f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bR+0OOX+WoeAtk8XQ40Q6t6FSoqFYf/Rz3WXMRYGtciFxzGIjy1lFoAL1w1NO5uPToz+JWHECMCqMd9y6CUPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:58:36.603806Z","bundle_sha256":"e043a186ff9a0232d63c1a5f4720ac509f0caaceb2fbec224f0d5c57e8867917"}}