{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4HR2T7A3NMCYM536BUAKNQ3QVQ","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":"ffd1b969b671c687e51693dcf7d340a5fd99aab5aaf77fd6fb6b90d7a006efe2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-26T11:02:21Z","title_canon_sha256":"190459323f49697cdd34735a6800f7ded545aac0b41e7088c584c364a6de13a2"},"schema_version":"1.0","source":{"id":"1407.7120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7120","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7120v2","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7120","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"4HR2T7A3NMCY","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4HR2T7A3NMCYM536","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4HR2T7A3","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:1b5d6b6fbb3990d88ce1b9beec4cffeb80120563b89506cce810cdfa9c9f5e90","target":"graph","created_at":"2026-05-18T02:45:48Z","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":"In this paper, among other results, we improve the best known estimates for the constants of the generalized Bohnenblust-Hille inequality. These enhancements are then used to improve the best known constants of the Hardy--Littlewood inequality; this inequality asserts that for a positive integer $m\\geq2$ with $2m\\leq p\\leq\\infty$ and $\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$ there exists a constant $C_{m,p}^{\\mathbb{K}}\\geq1$ such that, for all continuous $m$--linear forms $T:\\ell_{p}^{n}\\times\\cdots\\times\\ell_{p}^{n}\\rightarrow\\mathbb{K}$, and all positive integers $n$,% \\[ \\left( \\sum_{j_{1},.","authors_text":"Daniel Pellegrino, Gustavo Araujo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-26T11:02:21Z","title":"On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7120","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:e40f2fc7d2e927d17c756a822426879bc90db3cca70804904d37e4dd08f8d6f0","target":"record","created_at":"2026-05-18T02:45:48Z","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":"ffd1b969b671c687e51693dcf7d340a5fd99aab5aaf77fd6fb6b90d7a006efe2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-26T11:02:21Z","title_canon_sha256":"190459323f49697cdd34735a6800f7ded545aac0b41e7088c584c364a6de13a2"},"schema_version":"1.0","source":{"id":"1407.7120","kind":"arxiv","version":2}},"canonical_sha256":"e1e3a9fc1b6b0586777e0d00a6c370ac30d23f6794226ec455da55d3a82f1abc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1e3a9fc1b6b0586777e0d00a6c370ac30d23f6794226ec455da55d3a82f1abc","first_computed_at":"2026-05-18T02:45:48.280108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:48.280108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Dp2QEQdgffF+8Sm4GvgEyft1h4eaZ4La23YM3Wy8/spRDehBtrwybXx7bZ/6CZpisMUxlAfUHCxl8EpRkX1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:48.280601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e40f2fc7d2e927d17c756a822426879bc90db3cca70804904d37e4dd08f8d6f0","sha256:1b5d6b6fbb3990d88ce1b9beec4cffeb80120563b89506cce810cdfa9c9f5e90"],"state_sha256":"54bce198ac4dfb24ddf15ff431a62e638dd7519ec66b7e4a6101cd5de067d96f"}