{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SN2PTZWLVKFICPKQZKVM67M5LU","short_pith_number":"pith:SN2PTZWL","schema_version":"1.0","canonical_sha256":"9374f9e6cbaa8a813d50caaacf7d9d5d34e52fe1439888c1a2bfd901d26a1846","source":{"kind":"arxiv","id":"2603.02111","version":2},"attestation_state":"computed","paper":{"title":"Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Andrea Pinamonti, Boqing Xue, Dung The Tran, Thang Pham","submitted_at":"2026-03-02T17:28:02Z","abstract_excerpt":"Let $q$ be an odd prime power. We study Kakeya maximal operators associated with horizontal lines in the finite Heisenberg groups $\\mathbb H_n(\\mathbb F_q)$. Our principal object is the refined-direction maximal operator, whose parameter records the projective horizontal direction together with the central homogeneous coordinate determined by horizontality. In rank one, we prove \\[ \\|M_{\\mathbb H_1}^{\\mathrm{rd}}F\\|_{\\ell^2(\\mathcal D_1)} \\lesssim q^{\\frac{1}{2}} \\|F\\|_{\\ell^2(\\mathbb H_1(\\mathbb F_q))}, \\] where the exponent $\\frac{1}{2}$ is sharp. Combining this estimate with endpoint bounds"},"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":"2603.02111","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-02T17:28:02Z","cross_cats_sorted":["math.CA","math.GR","math.NT"],"title_canon_sha256":"5687ff50f776feeda89434fe7f8cf04b48dcd8c81d9122a74224512f0445d44f","abstract_canon_sha256":"f76381fd2ee299aa4584cf8328c2ea434773fcca4d42c860879d0624e0e38dca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:28.445621Z","signature_b64":"eeH3WVggPXR/mu9QW908XA+dXrDWmwVOJInJiVmXbAb/Q9a4qRhbssv8KZXx6OEzXEFevbXEZfDwP6SgjC5MCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9374f9e6cbaa8a813d50caaacf7d9d5d34e52fe1439888c1a2bfd901d26a1846","last_reissued_at":"2026-07-02T01:17:28.445167Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:28.445167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Andrea Pinamonti, Boqing Xue, Dung The Tran, Thang Pham","submitted_at":"2026-03-02T17:28:02Z","abstract_excerpt":"Let $q$ be an odd prime power. We study Kakeya maximal operators associated with horizontal lines in the finite Heisenberg groups $\\mathbb H_n(\\mathbb F_q)$. Our principal object is the refined-direction maximal operator, whose parameter records the projective horizontal direction together with the central homogeneous coordinate determined by horizontality. In rank one, we prove \\[ \\|M_{\\mathbb H_1}^{\\mathrm{rd}}F\\|_{\\ell^2(\\mathcal D_1)} \\lesssim q^{\\frac{1}{2}} \\|F\\|_{\\ell^2(\\mathbb H_1(\\mathbb F_q))}, \\] where the exponent $\\frac{1}{2}$ is sharp. Combining this estimate with endpoint bounds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.02111","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.02111/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":"2603.02111","created_at":"2026-07-02T01:17:28.445224+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.02111v2","created_at":"2026-07-02T01:17:28.445224+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.02111","created_at":"2026-07-02T01:17:28.445224+00:00"},{"alias_kind":"pith_short_12","alias_value":"SN2PTZWLVKFI","created_at":"2026-07-02T01:17:28.445224+00:00"},{"alias_kind":"pith_short_16","alias_value":"SN2PTZWLVKFICPKQ","created_at":"2026-07-02T01:17:28.445224+00:00"},{"alias_kind":"pith_short_8","alias_value":"SN2PTZWL","created_at":"2026-07-02T01:17:28.445224+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/SN2PTZWLVKFICPKQZKVM67M5LU","json":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU.json","graph_json":"https://pith.science/api/pith-number/SN2PTZWLVKFICPKQZKVM67M5LU/graph.json","events_json":"https://pith.science/api/pith-number/SN2PTZWLVKFICPKQZKVM67M5LU/events.json","paper":"https://pith.science/paper/SN2PTZWL"},"agent_actions":{"view_html":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU","download_json":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU.json","view_paper":"https://pith.science/paper/SN2PTZWL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.02111&json=true","fetch_graph":"https://pith.science/api/pith-number/SN2PTZWLVKFICPKQZKVM67M5LU/graph.json","fetch_events":"https://pith.science/api/pith-number/SN2PTZWLVKFICPKQZKVM67M5LU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU/action/storage_attestation","attest_author":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU/action/author_attestation","sign_citation":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU/action/citation_signature","submit_replication":"https://pith.science/pith/SN2PTZWLVKFICPKQZKVM67M5LU/action/replication_record"}},"created_at":"2026-07-02T01:17:28.445224+00:00","updated_at":"2026-07-02T01:17:28.445224+00:00"}