{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EUEGPEONGGUBWT5HZJOURI4XVV","short_pith_number":"pith:EUEGPEON","schema_version":"1.0","canonical_sha256":"25086791cd31a81b4fa7ca5d48a397ad78ad5cca9d5fbb58af0899117f2e4134","source":{"kind":"arxiv","id":"1009.2717","version":3},"attestation_state":"computed","paper":{"title":"Some improvements on the constants for the real Bohnenblust-Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Juan B. Seoane-Sep\\'ulveda","submitted_at":"2010-09-14T17:00:07Z","abstract_excerpt":"A classical inequality due to Bohnenblust and Hille states that for every $N \\in \\mathbb{N}$ and every $m$-linear mapping $U:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow\\mathbb{C}$ we have \\[(\\sum\\limits_{i_{1},...,i_{m}=1}^{N}| U(e_{i_{^{1}}},...,e_{i_{m}})| ^{\\frac{2m}{m+1}}) ^{\\frac{m+1}{2m}}\\leq C_{m}| U|] where $C_{m}=2^{\\frac{m-1}{2}}$. The result is also true for real Banach spaces. In this note we show that an adequate use of a recent new proof of Bohnenblust-Hille inequality, due to Defant, Popa and Schwarting, combined with the optimal constants of Khinchine's inequal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.2717","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-14T17:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"9481f8ba0ef2bb5b3175b7b941d7233c1ecbb13eba436cfa21771a1cb8933d5b","abstract_canon_sha256":"9bc51cc5c8a5f0f3c4155dfa6a4f0cbbd0db17557cbb27a075729226c3d2abf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:58.942707Z","signature_b64":"wGNO3XmbX5T1RkHrdBZay3JqUq+t4yq9gMEWcv8QoZpbiIy5nSXGVAcUDGDRu9lUQ2AxS26+91NBiStmzmgSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25086791cd31a81b4fa7ca5d48a397ad78ad5cca9d5fbb58af0899117f2e4134","last_reissued_at":"2026-05-18T04:39:58.942216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:58.942216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some improvements on the constants for the real Bohnenblust-Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Juan B. Seoane-Sep\\'ulveda","submitted_at":"2010-09-14T17:00:07Z","abstract_excerpt":"A classical inequality due to Bohnenblust and Hille states that for every $N \\in \\mathbb{N}$ and every $m$-linear mapping $U:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow\\mathbb{C}$ we have \\[(\\sum\\limits_{i_{1},...,i_{m}=1}^{N}| U(e_{i_{^{1}}},...,e_{i_{m}})| ^{\\frac{2m}{m+1}}) ^{\\frac{m+1}{2m}}\\leq C_{m}| U|] where $C_{m}=2^{\\frac{m-1}{2}}$. The result is also true for real Banach spaces. In this note we show that an adequate use of a recent new proof of Bohnenblust-Hille inequality, due to Defant, Popa and Schwarting, combined with the optimal constants of Khinchine's inequal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2717","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.2717","created_at":"2026-05-18T04:39:58.942291+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2717v3","created_at":"2026-05-18T04:39:58.942291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2717","created_at":"2026-05-18T04:39:58.942291+00:00"},{"alias_kind":"pith_short_12","alias_value":"EUEGPEONGGUB","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EUEGPEONGGUBWT5H","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EUEGPEON","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV","json":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV.json","graph_json":"https://pith.science/api/pith-number/EUEGPEONGGUBWT5HZJOURI4XVV/graph.json","events_json":"https://pith.science/api/pith-number/EUEGPEONGGUBWT5HZJOURI4XVV/events.json","paper":"https://pith.science/paper/EUEGPEON"},"agent_actions":{"view_html":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV","download_json":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV.json","view_paper":"https://pith.science/paper/EUEGPEON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2717&json=true","fetch_graph":"https://pith.science/api/pith-number/EUEGPEONGGUBWT5HZJOURI4XVV/graph.json","fetch_events":"https://pith.science/api/pith-number/EUEGPEONGGUBWT5HZJOURI4XVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV/action/storage_attestation","attest_author":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV/action/author_attestation","sign_citation":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV/action/citation_signature","submit_replication":"https://pith.science/pith/EUEGPEONGGUBWT5HZJOURI4XVV/action/replication_record"}},"created_at":"2026-05-18T04:39:58.942291+00:00","updated_at":"2026-05-18T04:39:58.942291+00:00"}