{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MC6BY54A7L4OU7NW4TQMALB2BJ","short_pith_number":"pith:MC6BY54A","schema_version":"1.0","canonical_sha256":"60bc1c7780faf8ea7db6e4e0c02c3a0a61eb120ab534722ae525ef6bf8a4750a","source":{"kind":"arxiv","id":"1605.03758","version":2},"attestation_state":"computed","paper":{"title":"Commutants of weighted shift directed graph operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David W. Kribs, Rupert H. Levene, Stephen C. Power","submitted_at":"2016-05-12T11:03:47Z","abstract_excerpt":"We consider non-selfadjoint operator algebras $\\mathfrak{L}(G,\\lambda)$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs $G$. These algebras may be viewed as noncommutative generalizations of weighted Bergman space algebras, or as weighted versions of the free semigroupoid algebras of directed graphs. A complete description of the commutant is obtained together with broad conditions that ensure the double commutant property. It is also shown that the double commutant property may fail for $\\mathfrak{L}(G,\\lambda)$ in the case of the single vertex"},"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":"1605.03758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-12T11:03:47Z","cross_cats_sorted":[],"title_canon_sha256":"847a76784979b38ac416a70e0acf8fe204593467c041b251c106e3478efaaff8","abstract_canon_sha256":"904c81af392e3f101c3000ecb1e892bfb2c53d861f4ea99295f3904885f3fd4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:44.013788Z","signature_b64":"z5u01SXZjOsmsWMBugezwH2K6eCGabZl2B+B2EJyt594EdDVaaEkaARVhas1NuyJoY8Xd7DWJmsnlq3fEUbQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60bc1c7780faf8ea7db6e4e0c02c3a0a61eb120ab534722ae525ef6bf8a4750a","last_reissued_at":"2026-05-18T00:07:44.012836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:44.012836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commutants of weighted shift directed graph operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David W. Kribs, Rupert H. Levene, Stephen C. Power","submitted_at":"2016-05-12T11:03:47Z","abstract_excerpt":"We consider non-selfadjoint operator algebras $\\mathfrak{L}(G,\\lambda)$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs $G$. These algebras may be viewed as noncommutative generalizations of weighted Bergman space algebras, or as weighted versions of the free semigroupoid algebras of directed graphs. A complete description of the commutant is obtained together with broad conditions that ensure the double commutant property. It is also shown that the double commutant property may fail for $\\mathfrak{L}(G,\\lambda)$ in the case of the single vertex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03758","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":"1605.03758","created_at":"2026-05-18T00:07:44.013012+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03758v2","created_at":"2026-05-18T00:07:44.013012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03758","created_at":"2026-05-18T00:07:44.013012+00:00"},{"alias_kind":"pith_short_12","alias_value":"MC6BY54A7L4O","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MC6BY54A7L4OU7NW","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MC6BY54A","created_at":"2026-05-18T12:30:32.724797+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/MC6BY54A7L4OU7NW4TQMALB2BJ","json":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ.json","graph_json":"https://pith.science/api/pith-number/MC6BY54A7L4OU7NW4TQMALB2BJ/graph.json","events_json":"https://pith.science/api/pith-number/MC6BY54A7L4OU7NW4TQMALB2BJ/events.json","paper":"https://pith.science/paper/MC6BY54A"},"agent_actions":{"view_html":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ","download_json":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ.json","view_paper":"https://pith.science/paper/MC6BY54A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03758&json=true","fetch_graph":"https://pith.science/api/pith-number/MC6BY54A7L4OU7NW4TQMALB2BJ/graph.json","fetch_events":"https://pith.science/api/pith-number/MC6BY54A7L4OU7NW4TQMALB2BJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ/action/storage_attestation","attest_author":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ/action/author_attestation","sign_citation":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ/action/citation_signature","submit_replication":"https://pith.science/pith/MC6BY54A7L4OU7NW4TQMALB2BJ/action/replication_record"}},"created_at":"2026-05-18T00:07:44.013012+00:00","updated_at":"2026-05-18T00:07:44.013012+00:00"}