{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VVFXCFJRURBAKMRQRJHS5PSGA6","short_pith_number":"pith:VVFXCFJR","schema_version":"1.0","canonical_sha256":"ad4b711531a4420532308a4f2ebe4607950950c97ac8854244de91e8cbe1a2d1","source":{"kind":"arxiv","id":"1809.06541","version":2},"attestation_state":"computed","paper":{"title":"Existence and exactness of exponential Riesz sequences and frames for fractal measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Chun-kit Lai, Dorin Ervin Dutkay, Shahram Emami","submitted_at":"2018-09-18T05:43:48Z","abstract_excerpt":"We study the construction of exponential frames and Riesz sequences for a class of fractal measures on ${\\mathbb R}^d$ generated by infinite convolution of discrete measures using the idea of frame towers and Riesz-sequence towers. The exactness and overcompleteness of the constructed exponential frame or Riesz sequence is completely classified in terms of the cardinality at each level of the tower. Using a version of the solution of the Kadison-Singer problem, known as the $R_{\\epsilon}$-conjecture, we show that all these measures contain exponential Riesz sequences of infinite cardinality. F"},"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":"1809.06541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-18T05:43:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"53ebe6605fc9e01ef9fe895d0a0b9174470c058382b14c432699a5684f7a7cd4","abstract_canon_sha256":"8c5dff9d5c7ca7c16abb8c4eb9ca556d1cfb15fd7f939b3c8506da4f32870c9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:32.165877Z","signature_b64":"dAhRadbRpbN3VHfOzNIO/LBD+hiEse4laUia9KSVPhii11CyTp7QdS2J/AQMGvS4VDkZtblQVVA4dtzHVabkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad4b711531a4420532308a4f2ebe4607950950c97ac8854244de91e8cbe1a2d1","last_reissued_at":"2026-05-17T23:44:32.165311Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:32.165311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and exactness of exponential Riesz sequences and frames for fractal measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Chun-kit Lai, Dorin Ervin Dutkay, Shahram Emami","submitted_at":"2018-09-18T05:43:48Z","abstract_excerpt":"We study the construction of exponential frames and Riesz sequences for a class of fractal measures on ${\\mathbb R}^d$ generated by infinite convolution of discrete measures using the idea of frame towers and Riesz-sequence towers. The exactness and overcompleteness of the constructed exponential frame or Riesz sequence is completely classified in terms of the cardinality at each level of the tower. Using a version of the solution of the Kadison-Singer problem, known as the $R_{\\epsilon}$-conjecture, we show that all these measures contain exponential Riesz sequences of infinite cardinality. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06541","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":"1809.06541","created_at":"2026-05-17T23:44:32.165413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.06541v2","created_at":"2026-05-17T23:44:32.165413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06541","created_at":"2026-05-17T23:44:32.165413+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVFXCFJRURBA","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVFXCFJRURBAKMRQ","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVFXCFJR","created_at":"2026-05-18T12:32:59.047623+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/VVFXCFJRURBAKMRQRJHS5PSGA6","json":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6.json","graph_json":"https://pith.science/api/pith-number/VVFXCFJRURBAKMRQRJHS5PSGA6/graph.json","events_json":"https://pith.science/api/pith-number/VVFXCFJRURBAKMRQRJHS5PSGA6/events.json","paper":"https://pith.science/paper/VVFXCFJR"},"agent_actions":{"view_html":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6","download_json":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6.json","view_paper":"https://pith.science/paper/VVFXCFJR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.06541&json=true","fetch_graph":"https://pith.science/api/pith-number/VVFXCFJRURBAKMRQRJHS5PSGA6/graph.json","fetch_events":"https://pith.science/api/pith-number/VVFXCFJRURBAKMRQRJHS5PSGA6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6/action/storage_attestation","attest_author":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6/action/author_attestation","sign_citation":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6/action/citation_signature","submit_replication":"https://pith.science/pith/VVFXCFJRURBAKMRQRJHS5PSGA6/action/replication_record"}},"created_at":"2026-05-17T23:44:32.165413+00:00","updated_at":"2026-05-17T23:44:32.165413+00:00"}