{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YXCNUHIQ34GJC5Q3OB4WCAGPQQ","short_pith_number":"pith:YXCNUHIQ","schema_version":"1.0","canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","source":{"kind":"arxiv","id":"1602.01821","version":1},"attestation_state":"computed","paper":{"title":"Sampling in de Branges Spaces and Naimark Dilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric S. Weber, Sa'ud al-Sa'di","submitted_at":"2016-02-04T20:34:31Z","abstract_excerpt":"We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These conditions are obtained by identifying the main construction with Naimark dilation of frames--embedding the de Branges space into a larger de Branges space while embedding the kernel functions associated with a sampling sequence into a Riesz basis for the larger space."},"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":"1602.01821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-04T20:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"efae10fa9ba1f5627f01716acfc683f191bf4323f2a9ef5d5d69fd01ea67de92","abstract_canon_sha256":"95d1263255ba47e16367c9f7285b2c6271cfee2b79c8db6c956b10798b55115f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:16.612114Z","signature_b64":"9I6OUYoZ1ZAcvtkQPvCUNrqnvZKMKaCTJoJLTaPtdwpDE9bMXYAvbW51GKblfWHosVrsIXOWDViw47zK736/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","last_reissued_at":"2026-05-18T01:21:16.611598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:16.611598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sampling in de Branges Spaces and Naimark Dilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric S. Weber, Sa'ud al-Sa'di","submitted_at":"2016-02-04T20:34:31Z","abstract_excerpt":"We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These conditions are obtained by identifying the main construction with Naimark dilation of frames--embedding the de Branges space into a larger de Branges space while embedding the kernel functions associated with a sampling sequence into a Riesz basis for the larger space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01821","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":"1602.01821","created_at":"2026-05-18T01:21:16.611682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.01821v1","created_at":"2026-05-18T01:21:16.611682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01821","created_at":"2026-05-18T01:21:16.611682+00:00"},{"alias_kind":"pith_short_12","alias_value":"YXCNUHIQ34GJ","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YXCNUHIQ34GJC5Q3","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YXCNUHIQ","created_at":"2026-05-18T12:30:53.716459+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/YXCNUHIQ34GJC5Q3OB4WCAGPQQ","json":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ.json","graph_json":"https://pith.science/api/pith-number/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/graph.json","events_json":"https://pith.science/api/pith-number/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/events.json","paper":"https://pith.science/paper/YXCNUHIQ"},"agent_actions":{"view_html":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ","download_json":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ.json","view_paper":"https://pith.science/paper/YXCNUHIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.01821&json=true","fetch_graph":"https://pith.science/api/pith-number/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/action/storage_attestation","attest_author":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/action/author_attestation","sign_citation":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/action/citation_signature","submit_replication":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/action/replication_record"}},"created_at":"2026-05-18T01:21:16.611682+00:00","updated_at":"2026-05-18T01:21:16.611682+00:00"}