{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:3MXFF4VVYT5RKDX7SGLXJWU4H2","short_pith_number":"pith:3MXFF4VV","schema_version":"1.0","canonical_sha256":"db2e52f2b5c4fb150eff919774da9c3e8c4587eb731e4f0334b12f676b480177","source":{"kind":"arxiv","id":"2411.19562","version":3},"attestation_state":"computed","paper":{"title":"On exponential frames near the critical density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jordy Timo van Velthoven, Marcin Bownik","submitted_at":"2024-11-29T09:15:00Z","abstract_excerpt":"Given a relatively compact set $\\Omega \\subseteq \\mathbb{R}$ of Lebesgue measure $|\\Omega|$ and $\\varepsilon > 0$, we show the existence of a set $\\Lambda \\subseteq \\mathbb{R}$ of uniform density $D (\\Lambda) \\leq (1+\\varepsilon) |\\Omega|$ such that the exponential system $\\{ \\exp(2\\pi i \\lambda \\cdot) \\mathbf{1}_{\\Omega}: \\lambda \\in \\Lambda \\}$ is a frame for $L^2 (\\Omega)$ with frame bounds $A |\\Omega|, B |\\Omega|$ for constants $A,B$ only depending on $\\varepsilon$. This solves a problem on the frame bounds of an exponential frame near the critical density posed by Nitzan, Olevskii and Ula"},"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":"2411.19562","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-29T09:15:00Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"17baacf12477fcb778f473081712765a2b3be941838943e2e0cc16511f4feb91","abstract_canon_sha256":"20e94c406c642c4c919c1b172e3ac3c34be70d6587f8ac765e81aa3219539a4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:49:11.487376Z","signature_b64":"oFx8nP539AoWI0W39wesmgtCOLe8p8DeNfa/x3E8DNELoDLhnLWwz08YtVRQ5SiBYlHm8WVQfno1h4D+2MnoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db2e52f2b5c4fb150eff919774da9c3e8c4587eb731e4f0334b12f676b480177","last_reissued_at":"2026-07-05T10:49:11.486960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:49:11.486960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On exponential frames near the critical density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jordy Timo van Velthoven, Marcin Bownik","submitted_at":"2024-11-29T09:15:00Z","abstract_excerpt":"Given a relatively compact set $\\Omega \\subseteq \\mathbb{R}$ of Lebesgue measure $|\\Omega|$ and $\\varepsilon > 0$, we show the existence of a set $\\Lambda \\subseteq \\mathbb{R}$ of uniform density $D (\\Lambda) \\leq (1+\\varepsilon) |\\Omega|$ such that the exponential system $\\{ \\exp(2\\pi i \\lambda \\cdot) \\mathbf{1}_{\\Omega}: \\lambda \\in \\Lambda \\}$ is a frame for $L^2 (\\Omega)$ with frame bounds $A |\\Omega|, B |\\Omega|$ for constants $A,B$ only depending on $\\varepsilon$. This solves a problem on the frame bounds of an exponential frame near the critical density posed by Nitzan, Olevskii and Ula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19562","kind":"arxiv","version":3},"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/2411.19562/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":"2411.19562","created_at":"2026-07-05T10:49:11.487020+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.19562v3","created_at":"2026-07-05T10:49:11.487020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19562","created_at":"2026-07-05T10:49:11.487020+00:00"},{"alias_kind":"pith_short_12","alias_value":"3MXFF4VVYT5R","created_at":"2026-07-05T10:49:11.487020+00:00"},{"alias_kind":"pith_short_16","alias_value":"3MXFF4VVYT5RKDX7","created_at":"2026-07-05T10:49:11.487020+00:00"},{"alias_kind":"pith_short_8","alias_value":"3MXFF4VV","created_at":"2026-07-05T10:49:11.487020+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/3MXFF4VVYT5RKDX7SGLXJWU4H2","json":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2.json","graph_json":"https://pith.science/api/pith-number/3MXFF4VVYT5RKDX7SGLXJWU4H2/graph.json","events_json":"https://pith.science/api/pith-number/3MXFF4VVYT5RKDX7SGLXJWU4H2/events.json","paper":"https://pith.science/paper/3MXFF4VV"},"agent_actions":{"view_html":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2","download_json":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2.json","view_paper":"https://pith.science/paper/3MXFF4VV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.19562&json=true","fetch_graph":"https://pith.science/api/pith-number/3MXFF4VVYT5RKDX7SGLXJWU4H2/graph.json","fetch_events":"https://pith.science/api/pith-number/3MXFF4VVYT5RKDX7SGLXJWU4H2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2/action/storage_attestation","attest_author":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2/action/author_attestation","sign_citation":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2/action/citation_signature","submit_replication":"https://pith.science/pith/3MXFF4VVYT5RKDX7SGLXJWU4H2/action/replication_record"}},"created_at":"2026-07-05T10:49:11.487020+00:00","updated_at":"2026-07-05T10:49:11.487020+00:00"}