{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OEEWNKPZ72YRI7QCLX2O5A3MB7","short_pith_number":"pith:OEEWNKPZ","schema_version":"1.0","canonical_sha256":"710966a9f9feb1147e025df4ee836c0fd166b4218a577522785d0c7db701b2c3","source":{"kind":"arxiv","id":"1603.01988","version":2},"attestation_state":"computed","paper":{"title":"Invariant subspaces generated by a single function in the polydisc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Beyaz Basak Koca, Nazim Sadik","submitted_at":"2016-03-07T09:58:14Z","abstract_excerpt":"In this study, we partially answer the question left open in Rudin's book \"Function theory in polydiscs\" on the structure of invariant subspaces of the Hardy space $H^2(U^n)$ on the polydisc $U^n$. We completely describe all invariant subspaces generated by a single function in the polydisc. Then, using our results, we give the unitary equivalence of this type of invariant subspace and a characterization of outer functions in $H^2(U^n)$."},"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":"1603.01988","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-07T09:58:14Z","cross_cats_sorted":[],"title_canon_sha256":"4d9b53c02391e2845ae84f791856ffb4fc7fbfb96a1fe47ded463cf7d90bb6a3","abstract_canon_sha256":"e95be005dde0e881ae5013ae9bf1d0fec56867be293f1a877c35a7cbff99cbcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:47.002465Z","signature_b64":"P6RupUiGTA94rq7UlNMh0xVQuxB/PQ7/hukLFdwzr+rg+ua7wLaB0O4s8hJyWF1QxtF4bdClLILHCdfSGa5ZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"710966a9f9feb1147e025df4ee836c0fd166b4218a577522785d0c7db701b2c3","last_reissued_at":"2026-05-18T00:18:47.001778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:47.001778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant subspaces generated by a single function in the polydisc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Beyaz Basak Koca, Nazim Sadik","submitted_at":"2016-03-07T09:58:14Z","abstract_excerpt":"In this study, we partially answer the question left open in Rudin's book \"Function theory in polydiscs\" on the structure of invariant subspaces of the Hardy space $H^2(U^n)$ on the polydisc $U^n$. We completely describe all invariant subspaces generated by a single function in the polydisc. Then, using our results, we give the unitary equivalence of this type of invariant subspace and a characterization of outer functions in $H^2(U^n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01988","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":"1603.01988","created_at":"2026-05-18T00:18:47.001891+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01988v2","created_at":"2026-05-18T00:18:47.001891+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01988","created_at":"2026-05-18T00:18:47.001891+00:00"},{"alias_kind":"pith_short_12","alias_value":"OEEWNKPZ72YR","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OEEWNKPZ72YRI7QC","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OEEWNKPZ","created_at":"2026-05-18T12:30:36.002864+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/OEEWNKPZ72YRI7QCLX2O5A3MB7","json":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7.json","graph_json":"https://pith.science/api/pith-number/OEEWNKPZ72YRI7QCLX2O5A3MB7/graph.json","events_json":"https://pith.science/api/pith-number/OEEWNKPZ72YRI7QCLX2O5A3MB7/events.json","paper":"https://pith.science/paper/OEEWNKPZ"},"agent_actions":{"view_html":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7","download_json":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7.json","view_paper":"https://pith.science/paper/OEEWNKPZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01988&json=true","fetch_graph":"https://pith.science/api/pith-number/OEEWNKPZ72YRI7QCLX2O5A3MB7/graph.json","fetch_events":"https://pith.science/api/pith-number/OEEWNKPZ72YRI7QCLX2O5A3MB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7/action/storage_attestation","attest_author":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7/action/author_attestation","sign_citation":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7/action/citation_signature","submit_replication":"https://pith.science/pith/OEEWNKPZ72YRI7QCLX2O5A3MB7/action/replication_record"}},"created_at":"2026-05-18T00:18:47.001891+00:00","updated_at":"2026-05-18T00:18:47.001891+00:00"}