{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TVAABGJHFLKWOSH3J4Z6YT5SCE","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":"42025dd6195c43dd79ec29af571027871b1a0be237b4fd9ae5bc0c9393d7a08c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-01-21T07:05:05Z","title_canon_sha256":"99dd960f834e02eb0dcb9ff02e9b3bcbb11a5eebfcb7248ced6da1553efda3ce"},"schema_version":"1.0","source":{"id":"2501.11928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.11928","created_at":"2026-07-05T10:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.11928v1","created_at":"2026-07-05T10:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.11928","created_at":"2026-07-05T10:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"TVAABGJHFLKW","created_at":"2026-07-05T10:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"TVAABGJHFLKWOSH3","created_at":"2026-07-05T10:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"TVAABGJH","created_at":"2026-07-05T10:03:16Z"}],"graph_snapshots":[{"event_id":"sha256:b5f5136e1d46787c317fccb0def8b8ba25278a63753b56c4b427bd211aef1e53","target":"graph","created_at":"2026-07-05T10:03:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.11928/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove \\( L^p \\) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \\( L^p \\) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group operations, to arbitrary matrices \\( A \\), investigating how the curvature induced by \\( A \\) governs the \\( L^p \\) boundedness of lacunary circular and elliptic maximal operators. Specifically, we provide necessary and sufficient conditions on \\( A \\) that determine whether these operators are bounded or unbounded on \\( L^p \\).","authors_text":"Jeongtae Oh, Joonil Kim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-01-21T07:05:05Z","title":"Lacunary elliptic maximal operator on the Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11928","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:b124e044635d116afb6120ed8f279920e0b04ffdd43ea76462e20e15ed6a0f0a","target":"record","created_at":"2026-07-05T10:03:16Z","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":"42025dd6195c43dd79ec29af571027871b1a0be237b4fd9ae5bc0c9393d7a08c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-01-21T07:05:05Z","title_canon_sha256":"99dd960f834e02eb0dcb9ff02e9b3bcbb11a5eebfcb7248ced6da1553efda3ce"},"schema_version":"1.0","source":{"id":"2501.11928","kind":"arxiv","version":1}},"canonical_sha256":"9d400099272ad56748fb4f33ec4fb2111b7672a2ac0e8c3ecc0f544a6601f445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d400099272ad56748fb4f33ec4fb2111b7672a2ac0e8c3ecc0f544a6601f445","first_computed_at":"2026-07-05T10:03:16.131779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:03:16.131779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K23zdMSyAv6BuFkmWbVq3JxrYt3LgurN//so+U2j2Wy53ZIu7PcNm+HO9mUAhBCFPLoVMZNGTk7hHfoqEhCKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:03:16.132223Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.11928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b124e044635d116afb6120ed8f279920e0b04ffdd43ea76462e20e15ed6a0f0a","sha256:b5f5136e1d46787c317fccb0def8b8ba25278a63753b56c4b427bd211aef1e53"],"state_sha256":"b032891eeb8240920d4a079511c30a61a781393af8c6fbece7748aa46fafe90d"}