{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WF2IYOTGHGCE27Z3LIFAN7ACLG","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":"d5c4bbd7a6697dd705e418eb90a3224cdb6e7671f243d30e4f8e789aaa82528c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-02T17:00:36Z","title_canon_sha256":"c7d1c4b1ebbc77ff6f2bd244103b659ea793752c29cab797e95e0bd7e8b6deb7"},"schema_version":"1.0","source":{"id":"1503.00618","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00618","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00618v2","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00618","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"pith_short_12","alias_value":"WF2IYOTGHGCE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WF2IYOTGHGCE27Z3","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WF2IYOTG","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:cdc4c29218b10a0fc44e019a1578b6c3550102a6245b6042e9504faf2b7125ea","target":"graph","created_at":"2026-05-18T00:19:48Z","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 investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known constants of the Clarkson inequality improves a recent result of Araujo et al. We also obtain the optimal constants of the generalized Hardy--Littlewood inequality in some special cases.","authors_text":"D.M. Serrano-Rodr\\'iguez, D. Nu\\~nez-Alarc\\'on, D. Pellegrino, J. Campos, V. F\\'avaro, W. Cavalcante","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-02T17:00:36Z","title":"Polynomial and multilinear Hardy--Littlewood inequalities: analytical and numerical approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00618","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":"sha256:3f389ba7f23c53d5ae88087671fb4a36586be4faf779e09a5c485d102724834d","target":"record","created_at":"2026-05-18T00:19:48Z","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":"d5c4bbd7a6697dd705e418eb90a3224cdb6e7671f243d30e4f8e789aaa82528c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-02T17:00:36Z","title_canon_sha256":"c7d1c4b1ebbc77ff6f2bd244103b659ea793752c29cab797e95e0bd7e8b6deb7"},"schema_version":"1.0","source":{"id":"1503.00618","kind":"arxiv","version":2}},"canonical_sha256":"b1748c3a6639844d7f3b5a0a06fc02598d562d34bf9f091aa548e500c8be13dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1748c3a6639844d7f3b5a0a06fc02598d562d34bf9f091aa548e500c8be13dc","first_computed_at":"2026-05-18T00:19:48.016100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:48.016100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1XvL6chfvRBfRAe+Uh06vSzUdaBPvCHoSbOiQmbtLlHTlo7uatujoSjDij6PrNlC667We2hnTH0JAQv4vdWmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:48.016827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00618","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f389ba7f23c53d5ae88087671fb4a36586be4faf779e09a5c485d102724834d","sha256:cdc4c29218b10a0fc44e019a1578b6c3550102a6245b6042e9504faf2b7125ea"],"state_sha256":"e6b3ea6f1575f3f4785a476d05b6202f49e4bb1277e98ac8e2fddfa3661dec4e"}