{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:YQPRRFPUPRXBPS4TYNJTIMEDJA","short_pith_number":"pith:YQPRRFPU","schema_version":"1.0","canonical_sha256":"c41f1895f47c6e17cb93c3533430834829d519e3a844b37b8f8904d0bc392f42","source":{"kind":"arxiv","id":"2404.05455","version":1},"attestation_state":"computed","paper":{"title":"Minimal gap for higher dimensional sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tanmoy Bera","submitted_at":"2024-04-08T12:39:31Z","abstract_excerpt":"In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for $(\\{\\boldsymbol{a}_n\\boldsymbol{\\alpha}\\}),$ $(\\{a_n\\boldsymbol{\\alpha}\\})$ and $(\\{\\boldsymbol{a}_n\\cdot\\boldsymbol{\\alpha}\\})$ in terms of cardinality of the difference set of $a_n$ and $\\boldsymbol{a}_n,$ where $a_n$ and $a_n^{(1)},\\dots,a_n^{(d)}$ are sequences of distinct integers."},"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":"2404.05455","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-04-08T12:39:31Z","cross_cats_sorted":[],"title_canon_sha256":"5448e5bd54db8ffb2f9b3da3f4296029a2110178cb72600fa3b6f75bd4bd166c","abstract_canon_sha256":"089ddd880a87fd647181e5cda61564b1687f94b642a15e0ba7d1b2307490b54c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:03:41.371127Z","signature_b64":"WMxfSDEl8ur9RSGERt1ijy0aaw/m//Q0x4SwRAjnfOCp69GtbuNJfK9xtmMjrnjfOgami3mzPxqtH7dQIUQ9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c41f1895f47c6e17cb93c3533430834829d519e3a844b37b8f8904d0bc392f42","last_reissued_at":"2026-06-08T01:03:41.370045Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:03:41.370045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal gap for higher dimensional sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tanmoy Bera","submitted_at":"2024-04-08T12:39:31Z","abstract_excerpt":"In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for $(\\{\\boldsymbol{a}_n\\boldsymbol{\\alpha}\\}),$ $(\\{a_n\\boldsymbol{\\alpha}\\})$ and $(\\{\\boldsymbol{a}_n\\cdot\\boldsymbol{\\alpha}\\})$ in terms of cardinality of the difference set of $a_n$ and $\\boldsymbol{a}_n,$ where $a_n$ and $a_n^{(1)},\\dots,a_n^{(d)}$ are sequences of distinct integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.05455","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/2404.05455/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":"2404.05455","created_at":"2026-06-08T01:03:41.370206+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.05455v1","created_at":"2026-06-08T01:03:41.370206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.05455","created_at":"2026-06-08T01:03:41.370206+00:00"},{"alias_kind":"pith_short_12","alias_value":"YQPRRFPUPRXB","created_at":"2026-06-08T01:03:41.370206+00:00"},{"alias_kind":"pith_short_16","alias_value":"YQPRRFPUPRXBPS4T","created_at":"2026-06-08T01:03:41.370206+00:00"},{"alias_kind":"pith_short_8","alias_value":"YQPRRFPU","created_at":"2026-06-08T01:03:41.370206+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/YQPRRFPUPRXBPS4TYNJTIMEDJA","json":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA.json","graph_json":"https://pith.science/api/pith-number/YQPRRFPUPRXBPS4TYNJTIMEDJA/graph.json","events_json":"https://pith.science/api/pith-number/YQPRRFPUPRXBPS4TYNJTIMEDJA/events.json","paper":"https://pith.science/paper/YQPRRFPU"},"agent_actions":{"view_html":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA","download_json":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA.json","view_paper":"https://pith.science/paper/YQPRRFPU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.05455&json=true","fetch_graph":"https://pith.science/api/pith-number/YQPRRFPUPRXBPS4TYNJTIMEDJA/graph.json","fetch_events":"https://pith.science/api/pith-number/YQPRRFPUPRXBPS4TYNJTIMEDJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA/action/storage_attestation","attest_author":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA/action/author_attestation","sign_citation":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA/action/citation_signature","submit_replication":"https://pith.science/pith/YQPRRFPUPRXBPS4TYNJTIMEDJA/action/replication_record"}},"created_at":"2026-06-08T01:03:41.370206+00:00","updated_at":"2026-06-08T01:03:41.370206+00:00"}