{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K4V3GIEUP7AFGR26MPAIDU7NEY","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":"cbc2ee9d6824981dc632cd47ba12ac4f35f51d4198599792a98328bbd913e889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-04T13:33:12Z","title_canon_sha256":"8c756a9e9d19e6c7e8dd7f9f9a90cbbbdda7aa8deac51141cf120774581b537d"},"schema_version":"1.0","source":{"id":"1401.0810","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0810","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0810v1","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0810","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"K4V3GIEUP7AF","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K4V3GIEUP7AFGR26","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K4V3GIEU","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:8cef024fecc2d549c360fa304caa66215ee87c197a2deea97d325dfd7bfcbe85","target":"graph","created_at":"2026-05-18T01:25:08Z","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":"In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a $W^*$-algebra. In particular the complex analytic manifold structure of these objects is investigated. The expressions on the Lie brackets for A and related algebroids are given in noncommutative operator coordinates in the explicit way. We also prove statements describing structure of the groupoid of partial isometries and the frame groupoid of A as well as the structure of their algebroids.","authors_text":"Anatol Odzijewicz, Aneta Sli\\.zewska, Grzegorz Jakimowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-04T13:33:12Z","title":"Algebroids associated to the groupoid of partially invertible elements of a $W^*$-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0810","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:eef7593daae50a645260b54f57be82d5298ea469277f3a8fd13acb29f41193e8","target":"record","created_at":"2026-05-18T01:25:08Z","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":"cbc2ee9d6824981dc632cd47ba12ac4f35f51d4198599792a98328bbd913e889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-04T13:33:12Z","title_canon_sha256":"8c756a9e9d19e6c7e8dd7f9f9a90cbbbdda7aa8deac51141cf120774581b537d"},"schema_version":"1.0","source":{"id":"1401.0810","kind":"arxiv","version":1}},"canonical_sha256":"572bb320947fc053475e63c081d3ed26236f88761e8a72bb1a9c8a53c5375bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"572bb320947fc053475e63c081d3ed26236f88761e8a72bb1a9c8a53c5375bdf","first_computed_at":"2026-05-18T01:25:08.779375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:08.779375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JFEWh/oFLLqsQME+kG3N6PrwvzfNCoVNNJyx5aUCXTyXzrGRpMq5D8vTDdUBYz43q3Xmg5tUG5yJDpBCPLCEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:08.779898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0810","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eef7593daae50a645260b54f57be82d5298ea469277f3a8fd13acb29f41193e8","sha256:8cef024fecc2d549c360fa304caa66215ee87c197a2deea97d325dfd7bfcbe85"],"state_sha256":"4cda550eabf7a4756c58516cab790f37b00243e39c6987047d9b31bfe9404d9e"}