{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:L6CJEMSIQCL5SJJNY2VPNS655A","short_pith_number":"pith:L6CJEMSI","schema_version":"1.0","canonical_sha256":"5f849232488097d9252dc6aaf6cbdde80fb199554259a6efd854a3c9afd1a8fe","source":{"kind":"arxiv","id":"1709.06637","version":2},"attestation_state":"computed","paper":{"title":"Structure of free semigroupoid algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Adam Dor-On, Boyu Li, Kenneth R. Davidson","submitted_at":"2017-09-19T20:31:43Z","abstract_excerpt":"A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atom"},"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":"1709.06637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-19T20:31:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d260b8bac5edae5e94147ff34553c8bbb13c5ef24fd15363593d7d49b7f65bea","abstract_canon_sha256":"5fc3178fb3d570436dd1a016df1455f8a2a43aa7a08eee5cd740720371d727f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:28.644327Z","signature_b64":"NWRh14el6ZRCw/CTkvUtThqbis7qU9vVBvMfd48V9X2yrBDESnNL3JbfOYeVOvU5wz1R28bVxHS3sGaehF88Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f849232488097d9252dc6aaf6cbdde80fb199554259a6efd854a3c9afd1a8fe","last_reissued_at":"2026-05-17T23:43:28.643712Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:28.643712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of free semigroupoid algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Adam Dor-On, Boyu Li, Kenneth R. Davidson","submitted_at":"2017-09-19T20:31:43Z","abstract_excerpt":"A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06637","kind":"arxiv","version":2},"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":"1709.06637","created_at":"2026-05-17T23:43:28.643821+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.06637v2","created_at":"2026-05-17T23:43:28.643821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06637","created_at":"2026-05-17T23:43:28.643821+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6CJEMSIQCL5","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6CJEMSIQCL5SJJN","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6CJEMSI","created_at":"2026-05-18T12:31:28.150371+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/L6CJEMSIQCL5SJJNY2VPNS655A","json":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A.json","graph_json":"https://pith.science/api/pith-number/L6CJEMSIQCL5SJJNY2VPNS655A/graph.json","events_json":"https://pith.science/api/pith-number/L6CJEMSIQCL5SJJNY2VPNS655A/events.json","paper":"https://pith.science/paper/L6CJEMSI"},"agent_actions":{"view_html":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A","download_json":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A.json","view_paper":"https://pith.science/paper/L6CJEMSI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.06637&json=true","fetch_graph":"https://pith.science/api/pith-number/L6CJEMSIQCL5SJJNY2VPNS655A/graph.json","fetch_events":"https://pith.science/api/pith-number/L6CJEMSIQCL5SJJNY2VPNS655A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A/action/storage_attestation","attest_author":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A/action/author_attestation","sign_citation":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A/action/citation_signature","submit_replication":"https://pith.science/pith/L6CJEMSIQCL5SJJNY2VPNS655A/action/replication_record"}},"created_at":"2026-05-17T23:43:28.643821+00:00","updated_at":"2026-05-17T23:43:28.643821+00:00"}