{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:M3VU2FBOWVTLWN32JMVMUF5LS6","short_pith_number":"pith:M3VU2FBO","schema_version":"1.0","canonical_sha256":"66eb4d142eb566bb377a4b2aca17ab978c30eeab3b91ee58ca72d4eee1173bc1","source":{"kind":"arxiv","id":"1712.09120","version":1},"attestation_state":"computed","paper":{"title":"On Gabor orthonormal bases over finite prime fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.CA","authors_text":"A. Iosevich, A. Mayeli, J. Pakianathan, M. Kolountzakis, Yu. Lyubarskii","submitted_at":"2017-12-25T19:40:56Z","abstract_excerpt":"We study Gabor orthonormal windows in $L^2({\\Bbb Z}_p^d)$ for translation and modulation sets $A$ and $B$, respectively, where $p$ is prime and $d\\geq 2$. We prove that for a set $E\\subset \\Bbb Z_p^d$, the indicator function $1_E$ is a Gabor window if and only if $E$ tiles and is spectral. Moreover, we prove that for any function $g:\\Bbb Z_p^d\\to \\Bbb C$ with support $E$, if the size of $E$ coincides with the size of the modulation set $B$ or if $g$ is positive, then $g$ is a unimodular function, i.e., $|g|=c1_E$, for some constant $c>0$, and $E$ tiles and is spectral. We also prove the existe"},"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":"1712.09120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-25T19:40:56Z","cross_cats_sorted":["math.CO","math.NT"],"title_canon_sha256":"044f35ce3509980c233ff1ee29e51ba374cf4f7ebe009b228bccb45a39c92a91","abstract_canon_sha256":"a6017c89e329a75036f175b2b091933af694be7b3e3c68874edc192e59115e04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:14.384255Z","signature_b64":"O3LQBbd4HBy3R6+SNYpmjOcrkH0BD2IJt/UXfkr+Vd4tpwN96dJjhJ28pFwljHrYBf3fLqaHdfUEJSGh3qbLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66eb4d142eb566bb377a4b2aca17ab978c30eeab3b91ee58ca72d4eee1173bc1","last_reissued_at":"2026-05-18T00:27:14.383787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:14.383787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Gabor orthonormal bases over finite prime fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.CA","authors_text":"A. Iosevich, A. Mayeli, J. Pakianathan, M. Kolountzakis, Yu. Lyubarskii","submitted_at":"2017-12-25T19:40:56Z","abstract_excerpt":"We study Gabor orthonormal windows in $L^2({\\Bbb Z}_p^d)$ for translation and modulation sets $A$ and $B$, respectively, where $p$ is prime and $d\\geq 2$. We prove that for a set $E\\subset \\Bbb Z_p^d$, the indicator function $1_E$ is a Gabor window if and only if $E$ tiles and is spectral. Moreover, we prove that for any function $g:\\Bbb Z_p^d\\to \\Bbb C$ with support $E$, if the size of $E$ coincides with the size of the modulation set $B$ or if $g$ is positive, then $g$ is a unimodular function, i.e., $|g|=c1_E$, for some constant $c>0$, and $E$ tiles and is spectral. We also prove the existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09120","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":""},"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":"1712.09120","created_at":"2026-05-18T00:27:14.383847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09120v1","created_at":"2026-05-18T00:27:14.383847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09120","created_at":"2026-05-18T00:27:14.383847+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3VU2FBOWVTL","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3VU2FBOWVTLWN32","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3VU2FBO","created_at":"2026-05-18T12:31:28.150371+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/M3VU2FBOWVTLWN32JMVMUF5LS6","json":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6.json","graph_json":"https://pith.science/api/pith-number/M3VU2FBOWVTLWN32JMVMUF5LS6/graph.json","events_json":"https://pith.science/api/pith-number/M3VU2FBOWVTLWN32JMVMUF5LS6/events.json","paper":"https://pith.science/paper/M3VU2FBO"},"agent_actions":{"view_html":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6","download_json":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6.json","view_paper":"https://pith.science/paper/M3VU2FBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09120&json=true","fetch_graph":"https://pith.science/api/pith-number/M3VU2FBOWVTLWN32JMVMUF5LS6/graph.json","fetch_events":"https://pith.science/api/pith-number/M3VU2FBOWVTLWN32JMVMUF5LS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6/action/storage_attestation","attest_author":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6/action/author_attestation","sign_citation":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6/action/citation_signature","submit_replication":"https://pith.science/pith/M3VU2FBOWVTLWN32JMVMUF5LS6/action/replication_record"}},"created_at":"2026-05-18T00:27:14.383847+00:00","updated_at":"2026-05-18T00:27:14.383847+00:00"}