{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NQCUVB45T5LE4Z3RASDVF3W3SP","short_pith_number":"pith:NQCUVB45","schema_version":"1.0","canonical_sha256":"6c054a879d9f564e6771048752eedb93de35d48ca7fba96474e71356422bfd76","source":{"kind":"arxiv","id":"1705.04166","version":2},"attestation_state":"computed","paper":{"title":"Multi-Window Weaving Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Markus Faulhuber, Monika D\\\"orfler","submitted_at":"2017-05-11T13:28:14Z","abstract_excerpt":"In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a Hilbert space norm criterion and a pointwise criterion in phase space. The key ingredient are localization operators in phase space and we give examples of woven multi-window Gabor frames consisting of Hermite functions."},"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":"1705.04166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-11T13:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"f4d65cb14427ba2de8185fbf56303739fca267bc51a573592573872837b73223","abstract_canon_sha256":"21e717051ab27c0227bcd0e5709e38e7eac3ef4be994bdc92cf1a78f52c4652a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:48.006633Z","signature_b64":"aOLdQLnyl64vCNI0GrsrjwCLcOaQ2LWSErHeVfH5WuecoBr0J8HgasWqza8xFg5oX9dymmJ0jufnkg/KcBpKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c054a879d9f564e6771048752eedb93de35d48ca7fba96474e71356422bfd76","last_reissued_at":"2026-05-18T00:13:48.005702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:48.005702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-Window Weaving Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Markus Faulhuber, Monika D\\\"orfler","submitted_at":"2017-05-11T13:28:14Z","abstract_excerpt":"In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a Hilbert space norm criterion and a pointwise criterion in phase space. The key ingredient are localization operators in phase space and we give examples of woven multi-window Gabor frames consisting of Hermite functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04166","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":"1705.04166","created_at":"2026-05-18T00:13:48.005868+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.04166v2","created_at":"2026-05-18T00:13:48.005868+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04166","created_at":"2026-05-18T00:13:48.005868+00:00"},{"alias_kind":"pith_short_12","alias_value":"NQCUVB45T5LE","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NQCUVB45T5LE4Z3R","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NQCUVB45","created_at":"2026-05-18T12:31:34.259226+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/NQCUVB45T5LE4Z3RASDVF3W3SP","json":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP.json","graph_json":"https://pith.science/api/pith-number/NQCUVB45T5LE4Z3RASDVF3W3SP/graph.json","events_json":"https://pith.science/api/pith-number/NQCUVB45T5LE4Z3RASDVF3W3SP/events.json","paper":"https://pith.science/paper/NQCUVB45"},"agent_actions":{"view_html":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP","download_json":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP.json","view_paper":"https://pith.science/paper/NQCUVB45","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.04166&json=true","fetch_graph":"https://pith.science/api/pith-number/NQCUVB45T5LE4Z3RASDVF3W3SP/graph.json","fetch_events":"https://pith.science/api/pith-number/NQCUVB45T5LE4Z3RASDVF3W3SP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP/action/storage_attestation","attest_author":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP/action/author_attestation","sign_citation":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP/action/citation_signature","submit_replication":"https://pith.science/pith/NQCUVB45T5LE4Z3RASDVF3W3SP/action/replication_record"}},"created_at":"2026-05-18T00:13:48.005868+00:00","updated_at":"2026-05-18T00:13:48.005868+00:00"}