{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2SBNS75CXSRUM4SPXTSUVQE7JT","short_pith_number":"pith:2SBNS75C","schema_version":"1.0","canonical_sha256":"d482d97fa2bca346724fbce54ac09f4cd70901652d4222eec2ef4d2ee65de0c5","source":{"kind":"arxiv","id":"2503.20259","version":1},"attestation_state":"computed","paper":{"title":"Gabor frames generated by Random-Periodic time-frequency shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sarthak Raj, S. Sivananthan","submitted_at":"2025-03-26T05:58:02Z","abstract_excerpt":"In this article, we consider a variation of the existence of Gabor frames in a probabilistic setting, in which we consider time-frequency shifts taken over random-periodic sets. We demonstrate that the method of selecting random-periodic time-frequency shifts is successful with high probability for specific categories of well-behaved functions, notably including Hermite functions, totally positive functions, and B-spline functions. In particular, we show that if $x_1, x_2, \\ldots ,x_m$ are independent and uniformly distributed in $[0,1),$ with $m$ sufficiently large, then the set of time-frequ"},"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":"2503.20259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-26T05:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"2471d22229993cba57762e0c2ea82c9d4a3d12cca298b51100e2b2a2f3c8e2f9","abstract_canon_sha256":"9f7a591ca257200fd20c8a618c9095a2ca69fd853118dc8dc4274c9eacd2d57d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:39:35.810136Z","signature_b64":"NnLdZYdHMh7ChB43Tyyy2+GwBSQF1JOeR/mgrXxvY76hhR1Qz29Upn4qgohwS/B2YRaJ8U0cQMTYvxrhTjGoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d482d97fa2bca346724fbce54ac09f4cd70901652d4222eec2ef4d2ee65de0c5","last_reissued_at":"2026-07-05T10:39:35.809601Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:39:35.809601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gabor frames generated by Random-Periodic time-frequency shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sarthak Raj, S. Sivananthan","submitted_at":"2025-03-26T05:58:02Z","abstract_excerpt":"In this article, we consider a variation of the existence of Gabor frames in a probabilistic setting, in which we consider time-frequency shifts taken over random-periodic sets. We demonstrate that the method of selecting random-periodic time-frequency shifts is successful with high probability for specific categories of well-behaved functions, notably including Hermite functions, totally positive functions, and B-spline functions. In particular, we show that if $x_1, x_2, \\ldots ,x_m$ are independent and uniformly distributed in $[0,1),$ with $m$ sufficiently large, then the set of time-frequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.20259","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/2503.20259/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":"2503.20259","created_at":"2026-07-05T10:39:35.809660+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.20259v1","created_at":"2026-07-05T10:39:35.809660+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.20259","created_at":"2026-07-05T10:39:35.809660+00:00"},{"alias_kind":"pith_short_12","alias_value":"2SBNS75CXSRU","created_at":"2026-07-05T10:39:35.809660+00:00"},{"alias_kind":"pith_short_16","alias_value":"2SBNS75CXSRUM4SP","created_at":"2026-07-05T10:39:35.809660+00:00"},{"alias_kind":"pith_short_8","alias_value":"2SBNS75C","created_at":"2026-07-05T10:39:35.809660+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.20746","citing_title":"Sampling properties of the zeroes of the Gaussian entire function","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT","json":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT.json","graph_json":"https://pith.science/api/pith-number/2SBNS75CXSRUM4SPXTSUVQE7JT/graph.json","events_json":"https://pith.science/api/pith-number/2SBNS75CXSRUM4SPXTSUVQE7JT/events.json","paper":"https://pith.science/paper/2SBNS75C"},"agent_actions":{"view_html":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT","download_json":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT.json","view_paper":"https://pith.science/paper/2SBNS75C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.20259&json=true","fetch_graph":"https://pith.science/api/pith-number/2SBNS75CXSRUM4SPXTSUVQE7JT/graph.json","fetch_events":"https://pith.science/api/pith-number/2SBNS75CXSRUM4SPXTSUVQE7JT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT/action/storage_attestation","attest_author":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT/action/author_attestation","sign_citation":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT/action/citation_signature","submit_replication":"https://pith.science/pith/2SBNS75CXSRUM4SPXTSUVQE7JT/action/replication_record"}},"created_at":"2026-07-05T10:39:35.809660+00:00","updated_at":"2026-07-05T10:39:35.809660+00:00"}