{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D6JYXDCUPN64GZJ3B5IHDW6XER","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":"b83708068fc19604309ee55d51e4520e508a201ef6ca3ba8229ab92692160186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-10T05:44:29Z","title_canon_sha256":"00f6717349931ad437ab125e4231a3e1ddf8405c3f677394f73f1d9f536c3d20"},"schema_version":"1.0","source":{"id":"1007.1701","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1701","created_at":"2026-05-18T04:30:02Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1701v3","created_at":"2026-05-18T04:30:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1701","created_at":"2026-05-18T04:30:02Z"},{"alias_kind":"pith_short_12","alias_value":"D6JYXDCUPN64","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D6JYXDCUPN64GZJ3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D6JYXDCU","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:3edb89cc85822947bc13647cd80530c79d29ac0d031052a93430cc12fa75ecb8","target":"graph","created_at":"2026-05-18T04:30:02Z","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 investigate the question of whether all elements of trace zero in a II_1-factor are single commutators. We show that all nilpotent elements are single commutators, as are all normal elements of trace zero whose spectral distributions are discrete measures. Some other classes of examples are considered.","authors_text":"Anna Skripka, Ken Dykema","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-10T05:44:29Z","title":"On single commutators in II_1-factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1701","kind":"arxiv","version":3},"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":"sha256:001dbb8d8e323c2af9bd16abbbb6c04b1da9ec1063e5101fb4bab80f30c973ee","target":"record","created_at":"2026-05-18T04:30:02Z","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":"b83708068fc19604309ee55d51e4520e508a201ef6ca3ba8229ab92692160186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-07-10T05:44:29Z","title_canon_sha256":"00f6717349931ad437ab125e4231a3e1ddf8405c3f677394f73f1d9f536c3d20"},"schema_version":"1.0","source":{"id":"1007.1701","kind":"arxiv","version":3}},"canonical_sha256":"1f938b8c547b7dc3653b0f5071dbd7247c9ea79fb1c823342f27dc4c3411adfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f938b8c547b7dc3653b0f5071dbd7247c9ea79fb1c823342f27dc4c3411adfc","first_computed_at":"2026-05-18T04:30:02.780474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:02.780474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GYZJxIPJYsreO9how5q1Ef3qL0rOQ6RLOyHYAhnE3F51KcHGKD3PoPJwJWx8aQ301fEm6ojkl1whu5/0uE7AAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:02.781098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1701","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:001dbb8d8e323c2af9bd16abbbb6c04b1da9ec1063e5101fb4bab80f30c973ee","sha256:3edb89cc85822947bc13647cd80530c79d29ac0d031052a93430cc12fa75ecb8"],"state_sha256":"7c60571437cc2149385fa2130c93823f297cbde5e26d5c0228acef8b4d9f1bd6"}