{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EPCWKCMFR2TTCAOQR7Q72RKBNU","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":"e0308cc6bad1facd00c84932f189f2998ab684227ad29bbeb493db00e3fd8ea4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-28T05:40:26Z","title_canon_sha256":"bf06952c01d5dfc1cb31e65aaeab58da65378b314dadba933b71ed28b300f6ea"},"schema_version":"1.0","source":{"id":"2502.20739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.20739","created_at":"2026-06-09T01:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2502.20739v2","created_at":"2026-06-09T01:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.20739","created_at":"2026-06-09T01:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"EPCWKCMFR2TT","created_at":"2026-06-09T01:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"EPCWKCMFR2TTCAOQ","created_at":"2026-06-09T01:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"EPCWKCMF","created_at":"2026-06-09T01:05:05Z"}],"graph_snapshots":[{"event_id":"sha256:0933695aefd5ad8da784e81d389db50e6c28c10b0befc75b9f6a9f38f8025449","target":"graph","created_at":"2026-06-09T01:05:05Z","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/2502.20739/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the lacunary spherical maximal operator, defined on the $n$-dimensional real hyperbolic space, is bounded on $L^p(\\H^n)$ for all $n\\ge2$ and $1<p\\le\\infty$. In particular, the lacunary set is significantly larger than its Euclidean counterpart, reflecting the influence of the geometry at infinity of the hyperbolic space.","authors_text":"Hong-Wei Zhang, Yunxiang Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-28T05:40:26Z","title":"Lacunary Spherical Maximal Operators on Hyperbolic Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20739","kind":"arxiv","version":2},"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":"sha256:5708aa1af0b239f29addbb920723780ea319193193dbefa7a32a41cee659e3ab","target":"record","created_at":"2026-06-09T01:05:05Z","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":"e0308cc6bad1facd00c84932f189f2998ab684227ad29bbeb493db00e3fd8ea4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-02-28T05:40:26Z","title_canon_sha256":"bf06952c01d5dfc1cb31e65aaeab58da65378b314dadba933b71ed28b300f6ea"},"schema_version":"1.0","source":{"id":"2502.20739","kind":"arxiv","version":2}},"canonical_sha256":"23c56509858ea73101d08fe1fd45416d2c226b9c375ffff310b6e9a2f6bf2fd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23c56509858ea73101d08fe1fd45416d2c226b9c375ffff310b6e9a2f6bf2fd5","first_computed_at":"2026-06-09T01:05:05.768528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:05.768528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1TtY3hNRR1D2Yai1G7echq131dEKraJoRPEtCnHxhzsA56J0xlm9WTIjomiN3SgeqMUyB/E+Sv9+oM5lTosoAg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:05.768996Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.20739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5708aa1af0b239f29addbb920723780ea319193193dbefa7a32a41cee659e3ab","sha256:0933695aefd5ad8da784e81d389db50e6c28c10b0befc75b9f6a9f38f8025449"],"state_sha256":"c806f5ccacc2c495e710e44e26514de04d17d0d84ca3a94831aff0b6c0c071f6"}