{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YKJUJDEONQRC25ERCLAT64WVKY","short_pith_number":"pith:YKJUJDEO","schema_version":"1.0","canonical_sha256":"c293448c8e6c222d749112c13f72d55604446bd5e0343e450faaf19593d74cb5","source":{"kind":"arxiv","id":"1706.04003","version":1},"attestation_state":"computed","paper":{"title":"Dual pair and Approximate dual for continuous frames in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asghar Rahimi, Bayaz Daraby, Zahra Darvishi","submitted_at":"2017-06-13T11:16:31Z","abstract_excerpt":"In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will be clarified through examples."},"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":"1706.04003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-13T11:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"67817418991be92a5ca6df520fcad4dd9ed241a1232bd056fedd5d0e32ce912b","abstract_canon_sha256":"735d3257e90773bd7ddb020540311d154fa4fb3cb06f64f8058acc4a8fad7a6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:24.765351Z","signature_b64":"s195ZlbJgyF8SRGjVz9K2CAJWnlx+SnCZXDTdEMvKTwY3wztkZlpwY26OBASIxBeVGyhbihdqrO0G7xhEMUJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c293448c8e6c222d749112c13f72d55604446bd5e0343e450faaf19593d74cb5","last_reissued_at":"2026-05-18T00:42:24.764763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:24.764763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dual pair and Approximate dual for continuous frames in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asghar Rahimi, Bayaz Daraby, Zahra Darvishi","submitted_at":"2017-06-13T11:16:31Z","abstract_excerpt":"In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will be clarified through examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04003","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":"1706.04003","created_at":"2026-05-18T00:42:24.764846+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.04003v1","created_at":"2026-05-18T00:42:24.764846+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04003","created_at":"2026-05-18T00:42:24.764846+00:00"},{"alias_kind":"pith_short_12","alias_value":"YKJUJDEONQRC","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YKJUJDEONQRC25ER","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YKJUJDEO","created_at":"2026-05-18T12:31:56.362134+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/YKJUJDEONQRC25ERCLAT64WVKY","json":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY.json","graph_json":"https://pith.science/api/pith-number/YKJUJDEONQRC25ERCLAT64WVKY/graph.json","events_json":"https://pith.science/api/pith-number/YKJUJDEONQRC25ERCLAT64WVKY/events.json","paper":"https://pith.science/paper/YKJUJDEO"},"agent_actions":{"view_html":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY","download_json":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY.json","view_paper":"https://pith.science/paper/YKJUJDEO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.04003&json=true","fetch_graph":"https://pith.science/api/pith-number/YKJUJDEONQRC25ERCLAT64WVKY/graph.json","fetch_events":"https://pith.science/api/pith-number/YKJUJDEONQRC25ERCLAT64WVKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY/action/storage_attestation","attest_author":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY/action/author_attestation","sign_citation":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY/action/citation_signature","submit_replication":"https://pith.science/pith/YKJUJDEONQRC25ERCLAT64WVKY/action/replication_record"}},"created_at":"2026-05-18T00:42:24.764846+00:00","updated_at":"2026-05-18T00:42:24.764846+00:00"}