{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WKRMI5BIJYLBD4SCJ22SWALXJG","short_pith_number":"pith:WKRMI5BI","canonical_record":{"source":{"id":"1301.4375","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-18T13:20:05Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"720543fb51fb2221738f4b0ed86afbc1c67f97f016b1a4348dce5119e14c794b","abstract_canon_sha256":"f4f8c0ff7385be4932b779516ea05586ed7fb334148fd41cebcea05f9af386bb"},"schema_version":"1.0"},"canonical_sha256":"b2a2c474284e1611f2424eb52b01774995fc38190d5aa92f58e57e2d5d6ac1bb","source":{"kind":"arxiv","id":"1301.4375","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4375","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4375v2","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4375","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"pith_short_12","alias_value":"WKRMI5BIJYLB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WKRMI5BIJYLBD4SC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WKRMI5BI","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WKRMI5BIJYLBD4SCJ22SWALXJG","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4375","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-18T13:20:05Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"720543fb51fb2221738f4b0ed86afbc1c67f97f016b1a4348dce5119e14c794b","abstract_canon_sha256":"f4f8c0ff7385be4932b779516ea05586ed7fb334148fd41cebcea05f9af386bb"},"schema_version":"1.0"},"canonical_sha256":"b2a2c474284e1611f2424eb52b01774995fc38190d5aa92f58e57e2d5d6ac1bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:29.029583Z","signature_b64":"X7KP9RLmqMIsI2cBNe8doNLX0HHAdqrI876Sx2cMiXG++MXf+isSN0OwxnsixXnCyl+fYISul9Kp2goOua5FBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2a2c474284e1611f2424eb52b01774995fc38190d5aa92f58e57e2d5d6ac1bb","last_reissued_at":"2026-05-18T01:37:29.028914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:29.028914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4375","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRfncJUpHqAWV6MKx2TTJvsizmM1UxEkdtKnoywSW4D/XRlzIDUANL0IojhToqMumIc0uKvnej9BUZWOvPmpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:19:51.597066Z"},"content_sha256":"b289712483a25239ac6b7f20ec3d2997cdf0bef16efdcad6f2f5e3e2877c9430","schema_version":"1.0","event_id":"sha256:b289712483a25239ac6b7f20ec3d2997cdf0bef16efdcad6f2f5e3e2877c9430"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WKRMI5BIJYLBD4SCJ22SWALXJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclicity in Dirichlet-type spaces and extremal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.CA","authors_text":"Alan Sola, Alberto Condori, Catherine B\\'en\\'eteau, Constanze Liaw, Daniel Seco","submitted_at":"2013-01-18T13:20:05Z","abstract_excerpt":"For functions $f$ in Dirichlet-type spaces we study how to determine constructively optimal polynomials $p_n$ that minimize $\\|p f-1\\|_\\alpha$ among all polynomials $p$ of degree at most $n$. Then we give upper and lower bounds for the rate of decay of $\\|p_{n}f-1\\|_{\\alpha}$ as $n$ approaches $\\infty$. Further, we study a generalization of a weak version of the Brown-Shields conjecture and some computational phenomena about the zeros of optimal polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4375","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0BWseHUhJwFX7uZLVlsmVe/swMMXbi30d5tLLIzAEhBsLxSrLi7/MZ6dn0iqKFhXDUYt902a2Z03wevKzR6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:19:51.597637Z"},"content_sha256":"f6a5760072e78130c53875ae2305f3fa599e9ff6a9a3ae2038c0015f87cf4822","schema_version":"1.0","event_id":"sha256:f6a5760072e78130c53875ae2305f3fa599e9ff6a9a3ae2038c0015f87cf4822"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKRMI5BIJYLBD4SCJ22SWALXJG/bundle.json","state_url":"https://pith.science/pith/WKRMI5BIJYLBD4SCJ22SWALXJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKRMI5BIJYLBD4SCJ22SWALXJG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T05:19:51Z","links":{"resolver":"https://pith.science/pith/WKRMI5BIJYLBD4SCJ22SWALXJG","bundle":"https://pith.science/pith/WKRMI5BIJYLBD4SCJ22SWALXJG/bundle.json","state":"https://pith.science/pith/WKRMI5BIJYLBD4SCJ22SWALXJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKRMI5BIJYLBD4SCJ22SWALXJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WKRMI5BIJYLBD4SCJ22SWALXJG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f4f8c0ff7385be4932b779516ea05586ed7fb334148fd41cebcea05f9af386bb","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-18T13:20:05Z","title_canon_sha256":"720543fb51fb2221738f4b0ed86afbc1c67f97f016b1a4348dce5119e14c794b"},"schema_version":"1.0","source":{"id":"1301.4375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4375","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4375v2","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4375","created_at":"2026-05-18T01:37:29Z"},{"alias_kind":"pith_short_12","alias_value":"WKRMI5BIJYLB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WKRMI5BIJYLBD4SC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WKRMI5BI","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:f6a5760072e78130c53875ae2305f3fa599e9ff6a9a3ae2038c0015f87cf4822","target":"graph","created_at":"2026-05-18T01:37:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For functions $f$ in Dirichlet-type spaces we study how to determine constructively optimal polynomials $p_n$ that minimize $\\|p f-1\\|_\\alpha$ among all polynomials $p$ of degree at most $n$. Then we give upper and lower bounds for the rate of decay of $\\|p_{n}f-1\\|_{\\alpha}$ as $n$ approaches $\\infty$. Further, we study a generalization of a weak version of the Brown-Shields conjecture and some computational phenomena about the zeros of optimal polynomials.","authors_text":"Alan Sola, Alberto Condori, Catherine B\\'en\\'eteau, Constanze Liaw, Daniel Seco","cross_cats":["math.CV","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-18T13:20:05Z","title":"Cyclicity in Dirichlet-type spaces and extremal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4375","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b289712483a25239ac6b7f20ec3d2997cdf0bef16efdcad6f2f5e3e2877c9430","target":"record","created_at":"2026-05-18T01:37:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f4f8c0ff7385be4932b779516ea05586ed7fb334148fd41cebcea05f9af386bb","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-18T13:20:05Z","title_canon_sha256":"720543fb51fb2221738f4b0ed86afbc1c67f97f016b1a4348dce5119e14c794b"},"schema_version":"1.0","source":{"id":"1301.4375","kind":"arxiv","version":2}},"canonical_sha256":"b2a2c474284e1611f2424eb52b01774995fc38190d5aa92f58e57e2d5d6ac1bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2a2c474284e1611f2424eb52b01774995fc38190d5aa92f58e57e2d5d6ac1bb","first_computed_at":"2026-05-18T01:37:29.028914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:29.028914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7KP9RLmqMIsI2cBNe8doNLX0HHAdqrI876Sx2cMiXG++MXf+isSN0OwxnsixXnCyl+fYISul9Kp2goOua5FBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:29.029583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b289712483a25239ac6b7f20ec3d2997cdf0bef16efdcad6f2f5e3e2877c9430","sha256:f6a5760072e78130c53875ae2305f3fa599e9ff6a9a3ae2038c0015f87cf4822"],"state_sha256":"48c80b4729e98ede3dcee757b7e2ffae716ec9c0d9fa76f05ce6e6bff98ed10c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tMjtBEKizkP/44V1ieDFOa0xAh+XUz07dBmrdHEqDg4MSM5FdWNNux/NheQW1cLIgtSq+wBQhCiNu6ooySVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:19:51.600353Z","bundle_sha256":"73f3b15a5a3828fa87dd43dc278af478869bac52a2522e3893b582dd6901d099"}}