{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HYEYHDQJVPYRUZMU6MYNUANBST","short_pith_number":"pith:HYEYHDQJ","schema_version":"1.0","canonical_sha256":"3e09838e09abf11a6594f330da01a194ffcc1e3283456585b8cc5ee381d36f85","source":{"kind":"arxiv","id":"1310.4094","version":1},"attestation_state":"computed","paper":{"title":"Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Alan A. Sola, Alberto A. Condori, Catherine B\\'en\\'eteau, Constanze Liaw, Daniel Seco","submitted_at":"2013-10-15T15:51:13Z","abstract_excerpt":"We study Dirichlet-type spaces $\\mathfrak{D}_{\\alpha}$ of analytic functions in the unit bidisk and their cyclic elements. These are the functions $f$ for which there exists a sequence $(p_n)_{n=1}^{\\infty}$ of polynomials in two variables such that $\\|p_nf-1\\|_{\\alpha}\\to 0$ as $n\\to \\infty$. We obtain a number of conditions that imply cyclicity, and obtain sharp estimates on the best possible rate of decay of the norms $\\|p_nf-1\\|_{\\alpha}$, in terms of the degree of $p_n$, for certain classes of functions using results concerning Hilbert spaces of functions of one complex variable and compa"},"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":"1310.4094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-15T15:51:13Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"bda583c479f5fde516171cd198efa32e085ec66fac5cf1c1a54753a94b3ba57c","abstract_canon_sha256":"cde59beb28c0067f7a97fe49269185c96fd8dbd10bb209149f0fdacd928045b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:28.938863Z","signature_b64":"BcHq+XvM9uIojmYgZzIQLzdAamFKLgd+YX9+eZqhA6+TXCO0NeqfNT2z3QMZWjljLfx4zxCbyCbm7Mp+IkczDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e09838e09abf11a6594f330da01a194ffcc1e3283456585b8cc5ee381d36f85","last_reissued_at":"2026-05-18T01:37:28.938421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:28.938421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Alan A. Sola, Alberto A. Condori, Catherine B\\'en\\'eteau, Constanze Liaw, Daniel Seco","submitted_at":"2013-10-15T15:51:13Z","abstract_excerpt":"We study Dirichlet-type spaces $\\mathfrak{D}_{\\alpha}$ of analytic functions in the unit bidisk and their cyclic elements. These are the functions $f$ for which there exists a sequence $(p_n)_{n=1}^{\\infty}$ of polynomials in two variables such that $\\|p_nf-1\\|_{\\alpha}\\to 0$ as $n\\to \\infty$. We obtain a number of conditions that imply cyclicity, and obtain sharp estimates on the best possible rate of decay of the norms $\\|p_nf-1\\|_{\\alpha}$, in terms of the degree of $p_n$, for certain classes of functions using results concerning Hilbert spaces of functions of one complex variable and compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4094","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":"1310.4094","created_at":"2026-05-18T01:37:28.938486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4094v1","created_at":"2026-05-18T01:37:28.938486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4094","created_at":"2026-05-18T01:37:28.938486+00:00"},{"alias_kind":"pith_short_12","alias_value":"HYEYHDQJVPYR","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HYEYHDQJVPYRUZMU","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HYEYHDQJ","created_at":"2026-05-18T12:27:46.883200+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/HYEYHDQJVPYRUZMU6MYNUANBST","json":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST.json","graph_json":"https://pith.science/api/pith-number/HYEYHDQJVPYRUZMU6MYNUANBST/graph.json","events_json":"https://pith.science/api/pith-number/HYEYHDQJVPYRUZMU6MYNUANBST/events.json","paper":"https://pith.science/paper/HYEYHDQJ"},"agent_actions":{"view_html":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST","download_json":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST.json","view_paper":"https://pith.science/paper/HYEYHDQJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4094&json=true","fetch_graph":"https://pith.science/api/pith-number/HYEYHDQJVPYRUZMU6MYNUANBST/graph.json","fetch_events":"https://pith.science/api/pith-number/HYEYHDQJVPYRUZMU6MYNUANBST/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST/action/storage_attestation","attest_author":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST/action/author_attestation","sign_citation":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST/action/citation_signature","submit_replication":"https://pith.science/pith/HYEYHDQJVPYRUZMU6MYNUANBST/action/replication_record"}},"created_at":"2026-05-18T01:37:28.938486+00:00","updated_at":"2026-05-18T01:37:28.938486+00:00"}