{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4GDAUCXEV4BGZCWK2WNED7XZFW","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":"643cea79785ee6bd2c647bec48bd44f007fa19280033bbad9240d3dbc1406045","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-01-30T08:49:50Z","title_canon_sha256":"7d121b52883f7513e9f5c9c5472399e2b22abc1707312bc204c235dafd932a60"},"schema_version":"1.0","source":{"id":"1901.10711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10711","created_at":"2026-05-17T23:55:06Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10711v1","created_at":"2026-05-17T23:55:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10711","created_at":"2026-05-17T23:55:06Z"},{"alias_kind":"pith_short_12","alias_value":"4GDAUCXEV4BG","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4GDAUCXEV4BGZCWK","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4GDAUCXE","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:dddb7c2313dfaffcee53a36a7432473979cf32e95ee3b895f770c19f467c1915","target":"graph","created_at":"2026-05-17T23:55:06Z","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 show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type II$_1$, settling a question, in the negative, that had puzzled a number of us.","authors_text":"Andreas Thom, Richard V. Kadison, Zhe Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-01-30T08:49:50Z","title":"A note on commutators in algebras of unbounded operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10711","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":"sha256:46b52038dc32c7a2c1fa781bd70ddbbbaf0f619966e657edad3e00bd6553abf2","target":"record","created_at":"2026-05-17T23:55:06Z","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":"643cea79785ee6bd2c647bec48bd44f007fa19280033bbad9240d3dbc1406045","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-01-30T08:49:50Z","title_canon_sha256":"7d121b52883f7513e9f5c9c5472399e2b22abc1707312bc204c235dafd932a60"},"schema_version":"1.0","source":{"id":"1901.10711","kind":"arxiv","version":1}},"canonical_sha256":"e1860a0ae4af026c8acad59a41fef92d93f0fb4bbd8be8dc667d668524bcd3ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1860a0ae4af026c8acad59a41fef92d93f0fb4bbd8be8dc667d668524bcd3ec","first_computed_at":"2026-05-17T23:55:06.205627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:06.205627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RbuDOlKP1HWt6U4UvBOoFp1SIeU8nf6Lj7ESe5mEDSzpJFy9YkLycgQ/kqT0sgjqsWyIiAJFJR9WBpkVYM7+CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:06.206242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46b52038dc32c7a2c1fa781bd70ddbbbaf0f619966e657edad3e00bd6553abf2","sha256:dddb7c2313dfaffcee53a36a7432473979cf32e95ee3b895f770c19f467c1915"],"state_sha256":"0a35840f760ca459eab205256128eadb038b3359a9958875c36db9850f99a979"}