{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HS6VVOPMD356TF2NNCB43UZ2ID","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":"4f9d32045860e782d3b0822f51ef4ea3d099b14d113d1ab349249b04d0a62254","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-26T18:30:05Z","title_canon_sha256":"f9b475e731b977aa4bee19f13deef09d5ced1c7fe1636fa154ac8548629dd667"},"schema_version":"1.0","source":{"id":"1501.06513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06513","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06513v1","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06513","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"HS6VVOPMD356","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HS6VVOPMD356TF2N","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HS6VVOPM","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:e122391712f398b6a3f625c2ab4903bb4aff4c289cc947a8000bf51459bd4052","target":"graph","created_at":"2026-05-18T02:28:41Z","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"},"paper":{"abstract_excerpt":"We establish Hardy--Littlewood inequalities for the Heckman--Opdam transform associated to a general root datum $(\\mathfrak{a},\\Sigma,m)$ that generalizes an analogous result for the spherical Fourier transform on a Riemannian symmetric space of the non-compact type due to Eguchi and Kumahara. In particular we obtain a more precise Hausdorff--Young inequality that generalizes a recent result due to Narayanan, Pasquale, and Pusti.","authors_text":"Troels Roussau Johansen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-26T18:30:05Z","title":"Hardy--Littlewood inequalities for the Heckman--Opdam transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06513","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:cf4fa3f64960a4d2e998f0257028e5e3e0f2fbe9d0f28a06a4e0d245d22ec9e2","target":"record","created_at":"2026-05-18T02:28:41Z","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":"4f9d32045860e782d3b0822f51ef4ea3d099b14d113d1ab349249b04d0a62254","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-26T18:30:05Z","title_canon_sha256":"f9b475e731b977aa4bee19f13deef09d5ced1c7fe1636fa154ac8548629dd667"},"schema_version":"1.0","source":{"id":"1501.06513","kind":"arxiv","version":1}},"canonical_sha256":"3cbd5ab9ec1efbe9974d6883cdd33a40cb50bf8580f366e8303611fdde1b64a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cbd5ab9ec1efbe9974d6883cdd33a40cb50bf8580f366e8303611fdde1b64a6","first_computed_at":"2026-05-18T02:28:41.145952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:41.145952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/By/6JUACOLqBl+PLaK0lWN5WcbNlXkJJy0NeQxpGcLENEqAcYWOtAmFnpoeII4yO9Xr4peiw+mOhOLamWyNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:41.146373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf4fa3f64960a4d2e998f0257028e5e3e0f2fbe9d0f28a06a4e0d245d22ec9e2","sha256:e122391712f398b6a3f625c2ab4903bb4aff4c289cc947a8000bf51459bd4052"],"state_sha256":"f176d3966310a2b0146f35eb0f5704f21bdc904fabb9be32d9f0e60948ae0d2f"}