{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5DYMO5IL25N2D5KYEKQJKH3QUO","short_pith_number":"pith:5DYMO5IL","schema_version":"1.0","canonical_sha256":"e8f0c7750bd75ba1f55822a0951f70a39c9cbbb9a0db89301d1d24564af5c9bf","source":{"kind":"arxiv","id":"2606.26052","version":1},"attestation_state":"computed","paper":{"title":"On the existence problem of regular Gabor frames","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor","submitted_at":"2026-06-24T17:30:14Z","abstract_excerpt":"For every dimension $d > 1$, we establish explicit criteria on lattices $\\Lambda \\subset \\mathbb{R}^{2d}$ with density $D(\\Lambda) > 1$ such that no function with a continuous Zak transform generates a Gabor frame along $\\Lambda$. In particular, this gives a negative answer to the existence problem of Gabor frames with window functions in the Schwartz space, the Feichtinger algebra, and the Fourier-invariant Wiener space. Our result is based on a characterization of when a collection of quasiperiodic functions admits a common zero, which may be of independent interest. We also include a formal"},"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":"2606.26052","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-06-24T17:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"c2ddd10022289d7b58ffd2d6bd1d5e4861cb78940a1064803f067fd8c2a8608b","abstract_canon_sha256":"7f2be87fe31417a5ce72f45838c711ff2cc00a8b186ce5c9524a8082ca791c4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:47.113731Z","signature_b64":"eouJZlVzFgJnLCsPU5hC9A1jPNFIjZPB4CQBPAc9ZL6kcBzgC5G6IeZCJ1WGNPKXu+MAbWhNbzhuL80MbRLYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8f0c7750bd75ba1f55822a0951f70a39c9cbbb9a0db89301d1d24564af5c9bf","last_reissued_at":"2026-06-25T01:18:47.113351Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:47.113351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence problem of regular Gabor frames","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor","submitted_at":"2026-06-24T17:30:14Z","abstract_excerpt":"For every dimension $d > 1$, we establish explicit criteria on lattices $\\Lambda \\subset \\mathbb{R}^{2d}$ with density $D(\\Lambda) > 1$ such that no function with a continuous Zak transform generates a Gabor frame along $\\Lambda$. In particular, this gives a negative answer to the existence problem of Gabor frames with window functions in the Schwartz space, the Feichtinger algebra, and the Fourier-invariant Wiener space. Our result is based on a characterization of when a collection of quasiperiodic functions admits a common zero, which may be of independent interest. We also include a formal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26052","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26052/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.26052","created_at":"2026-06-25T01:18:47.113413+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.26052v1","created_at":"2026-06-25T01:18:47.113413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26052","created_at":"2026-06-25T01:18:47.113413+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DYMO5IL25N2","created_at":"2026-06-25T01:18:47.113413+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DYMO5IL25N2D5KY","created_at":"2026-06-25T01:18:47.113413+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DYMO5IL","created_at":"2026-06-25T01:18:47.113413+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/5DYMO5IL25N2D5KYEKQJKH3QUO","json":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO.json","graph_json":"https://pith.science/api/pith-number/5DYMO5IL25N2D5KYEKQJKH3QUO/graph.json","events_json":"https://pith.science/api/pith-number/5DYMO5IL25N2D5KYEKQJKH3QUO/events.json","paper":"https://pith.science/paper/5DYMO5IL"},"agent_actions":{"view_html":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO","download_json":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO.json","view_paper":"https://pith.science/paper/5DYMO5IL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.26052&json=true","fetch_graph":"https://pith.science/api/pith-number/5DYMO5IL25N2D5KYEKQJKH3QUO/graph.json","fetch_events":"https://pith.science/api/pith-number/5DYMO5IL25N2D5KYEKQJKH3QUO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO/action/storage_attestation","attest_author":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO/action/author_attestation","sign_citation":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO/action/citation_signature","submit_replication":"https://pith.science/pith/5DYMO5IL25N2D5KYEKQJKH3QUO/action/replication_record"}},"created_at":"2026-06-25T01:18:47.113413+00:00","updated_at":"2026-06-25T01:18:47.113413+00:00"}