{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:X2YT4QLU7U7VGLXCS335FGFKUF","short_pith_number":"pith:X2YT4QLU","schema_version":"1.0","canonical_sha256":"beb13e4174fd3f532ee296f7d298aaa15610940db42dc60aff80aa85f3b350f2","source":{"kind":"arxiv","id":"1404.5414","version":1},"attestation_state":"computed","paper":{"title":"Multiplication operators defined by a class of polynomials on L_a^2(D^2)","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hansong Huang, Hui Dan","submitted_at":"2014-04-22T08:11:52Z","abstract_excerpt":"In this paper, we consider those multiplication operators M_p on the Bergman space L_a^2(D^2) over the bidisk, defined by a class of polynomials p. Also, this paper consider the reducing subspaces of M_p, the von Neumann algebra W^*(p) generated by M_p, and its commutant V^*(p)=W^*(p)'. The structure of V^*(p) is completely determined, along with those reducing subspaces of M_p."},"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":"1404.5414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OA","submitted_at":"2014-04-22T08:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"e709c9538fc569ec1b4de9a1c8038bd9fba5d2133cdbec57f4ed64c3fac989f5","abstract_canon_sha256":"13abf8d2c5152cb72649ec871bd7e1990fbd0f57223c3d69476033fa390ce092"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:31.507273Z","signature_b64":"0FzTXrjb57s0YrCbsPcYkNNSJOSwLk5JSgDZIyRLrrMgucT+GtJlIAs6IlMxcms1gCfrLWv5J4fwYRSCbfXyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beb13e4174fd3f532ee296f7d298aaa15610940db42dc60aff80aa85f3b350f2","last_reissued_at":"2026-05-18T02:53:31.506146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:31.506146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplication operators defined by a class of polynomials on L_a^2(D^2)","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Hansong Huang, Hui Dan","submitted_at":"2014-04-22T08:11:52Z","abstract_excerpt":"In this paper, we consider those multiplication operators M_p on the Bergman space L_a^2(D^2) over the bidisk, defined by a class of polynomials p. Also, this paper consider the reducing subspaces of M_p, the von Neumann algebra W^*(p) generated by M_p, and its commutant V^*(p)=W^*(p)'. The structure of V^*(p) is completely determined, along with those reducing subspaces of M_p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5414","kind":"arxiv","version":1},"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":"1404.5414","created_at":"2026-05-18T02:53:31.506339+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5414v1","created_at":"2026-05-18T02:53:31.506339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5414","created_at":"2026-05-18T02:53:31.506339+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2YT4QLU7U7V","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2YT4QLU7U7VGLXC","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2YT4QLU","created_at":"2026-05-18T12:28:54.890064+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/X2YT4QLU7U7VGLXCS335FGFKUF","json":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF.json","graph_json":"https://pith.science/api/pith-number/X2YT4QLU7U7VGLXCS335FGFKUF/graph.json","events_json":"https://pith.science/api/pith-number/X2YT4QLU7U7VGLXCS335FGFKUF/events.json","paper":"https://pith.science/paper/X2YT4QLU"},"agent_actions":{"view_html":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF","download_json":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF.json","view_paper":"https://pith.science/paper/X2YT4QLU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5414&json=true","fetch_graph":"https://pith.science/api/pith-number/X2YT4QLU7U7VGLXCS335FGFKUF/graph.json","fetch_events":"https://pith.science/api/pith-number/X2YT4QLU7U7VGLXCS335FGFKUF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF/action/storage_attestation","attest_author":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF/action/author_attestation","sign_citation":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF/action/citation_signature","submit_replication":"https://pith.science/pith/X2YT4QLU7U7VGLXCS335FGFKUF/action/replication_record"}},"created_at":"2026-05-18T02:53:31.506339+00:00","updated_at":"2026-05-18T02:53:31.506339+00:00"}