{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YQE4JR2NMCJCAVQSCB7VIW43TL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"27273aa8e1e8eaa34d8bda0b9bbdcd6c03fca16c7526dece26ea1fc33e31f0bf","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-12T18:34:06Z","title_canon_sha256":"53c15ce8cd578a5a4a0b441bd71ca5937da0b881ce5bd172b4ebcd3517afaf0e"},"schema_version":"1.0","source":{"id":"1108.2684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2684","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2684v1","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2684","created_at":"2026-05-18T04:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"YQE4JR2NMCJC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YQE4JR2NMCJCAVQS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YQE4JR2N","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:e09caaedf114e640cd7b000429ebc98698ac449389221ca1b3fb229b823ff589","target":"graph","created_at":"2026-05-18T04:15:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the frame property of the Gabor system G(g, {\\alpha}, {\\beta}) = {e2{\\pi}i{\\beta}nt g(t - {\\alpha}m) : m, n \\in Z} for the case of rational oversampling, i.e. {\\alpha}, {\\beta} \\in Q. A 'rational' analogue of the Ron-Shen Gramian is constructed, and prove that for any odd window function g the system G(g, {\\alpha}, {\\beta}) does not generate a frame if {\\alpha}{\\beta} = (n-1)/n. Special attention is paid to the first Hermite function h_1(t) = te^(-{\\pi}t^2).","authors_text":"Preben Gr{\\aa}berg Nes, Yurii Lyubarskii","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-12T18:34:06Z","title":"Gabor frames with rational density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2684","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:34e502e8ca609e8714cbda3ffb1ddfa82ff8784c2d803ca77d8519dc828e54c5","target":"record","created_at":"2026-05-18T04:15:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"27273aa8e1e8eaa34d8bda0b9bbdcd6c03fca16c7526dece26ea1fc33e31f0bf","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-12T18:34:06Z","title_canon_sha256":"53c15ce8cd578a5a4a0b441bd71ca5937da0b881ce5bd172b4ebcd3517afaf0e"},"schema_version":"1.0","source":{"id":"1108.2684","kind":"arxiv","version":1}},"canonical_sha256":"c409c4c74d6092205612107f545b9b9ac46c7292e270b3ca77361cf5d4c5c29c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c409c4c74d6092205612107f545b9b9ac46c7292e270b3ca77361cf5d4c5c29c","first_computed_at":"2026-05-18T04:15:36.418389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:36.418389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QVM2kjg8ty22MT+wK3hZehQfGJMwOaXwVJG6oaeoE5xJdmXOkoDKYkVCyGWrlndHivqMkbtwoc9vYFLvBtkiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:36.418760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34e502e8ca609e8714cbda3ffb1ddfa82ff8784c2d803ca77d8519dc828e54c5","sha256:e09caaedf114e640cd7b000429ebc98698ac449389221ca1b3fb229b823ff589"],"state_sha256":"7e0e7a5003c3803f6fcff4e66f826a36254fce0d23f348c0613a2ad594f93032"}