{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R42ZDRGEB4AAGNPCGY2YO3UGBK","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":"828a6e958aea0a1a2b9d1d999f75ff38c549d30749b68081ba257a74a01292a9","cross_cats_sorted":["cs.IT","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-23T13:00:29Z","title_canon_sha256":"8ff84954ec0d0b9b1e4db3ed10aaae2ebd14016a370a5ba23132c2cfdf19e4c5"},"schema_version":"1.0","source":{"id":"1808.07732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07732","created_at":"2026-05-18T00:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07732v1","created_at":"2026-05-18T00:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07732","created_at":"2026-05-18T00:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"R42ZDRGEB4AA","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R42ZDRGEB4AAGNPC","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R42ZDRGE","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:92fe4562b6afcef1c20167240c328ec7cf115e11aa3c508e295a858d957c3ecf","target":"graph","created_at":"2026-05-18T00:07:24Z","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":"In this paper, we proved an exact asymptotically sharp upper bound of the $L^p$ Lebesgue Constant (i.e. the $L^p$ norm of Dirichlet kernel) for $p\\ge 2$. As an application, we also verified the implication of a new $\\infty $-R\\'enyi entropy power inequality for integer valued random variables.","authors_text":"James Melbourne, Mokshay Madiman, Peng Xu","cross_cats":["cs.IT","math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-23T13:00:29Z","title":"An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\\infty$-R\\'enyi Entropy Power Inequality for Integer Valued Random Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07732","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":"sha256:59f98fe762366cd5dff9ab0f7d34becdf6e10e8e187a06aa82c4afb7f798a8a2","target":"record","created_at":"2026-05-18T00:07:24Z","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":"828a6e958aea0a1a2b9d1d999f75ff38c549d30749b68081ba257a74a01292a9","cross_cats_sorted":["cs.IT","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-23T13:00:29Z","title_canon_sha256":"8ff84954ec0d0b9b1e4db3ed10aaae2ebd14016a370a5ba23132c2cfdf19e4c5"},"schema_version":"1.0","source":{"id":"1808.07732","kind":"arxiv","version":1}},"canonical_sha256":"8f3591c4c40f000335e23635876e860a9487e04aac392dd9e2eca6fa3c4b0b18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f3591c4c40f000335e23635876e860a9487e04aac392dd9e2eca6fa3c4b0b18","first_computed_at":"2026-05-18T00:07:24.423221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:24.423221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gGvUzJ8c1ChJ8uFiUC9XB3n8NDBPluWPqpE/W1uEHKdFpHG38aoNuzmNzJxWicqeonaKmeapWDXnPcgzL9bsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:24.423807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59f98fe762366cd5dff9ab0f7d34becdf6e10e8e187a06aa82c4afb7f798a8a2","sha256:92fe4562b6afcef1c20167240c328ec7cf115e11aa3c508e295a858d957c3ecf"],"state_sha256":"1826bbdbc7ba9c97a4b8b3b1bb9150cb19a691bb2e86ebdb1222b8dcee756e4b"}