{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MDIXIYR26HWFLUFREKBNL54DIM","short_pith_number":"pith:MDIXIYR2","schema_version":"1.0","canonical_sha256":"60d174623af1ec55d0b12282d5f783432855c94695eab0f3d39dd245ff04c06f","source":{"kind":"arxiv","id":"1107.4814","version":1},"attestation_state":"computed","paper":{"title":"Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Pellegrino, G. A. Mu\\~noz-Fern\\'andez, J. B. Seoane-Sep\\'ulveda","submitted_at":"2011-07-24T23:52:30Z","abstract_excerpt":"A classical inequality due to H.F. Bohnenblust and E. Hille states that for every positive integer $n$ there is a constant $C_{n}>0$ so that $$(\\sum\\limits_{i_{1},...,i_{n}=1}^{N}|U(e_{i_{^{1}}},...,e_{i_{n}})|^{\\frac{2n}{n+1}})^{\\frac{n+1}{2n}}\\leq C_{n}||U||$$ for every positive integer $N$ and every $n$-linear mapping $U:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow\\mathbb{C}$. The original estimates for those constants from Bohnenblust and Hille are $$C_{n}=n^{\\frac{n+1}{2n}}2^{\\frac{n-1}{2}}.$$ In this note we present explicit formulae for quite better constants, and calcul"},"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":"1107.4814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-24T23:52:30Z","cross_cats_sorted":[],"title_canon_sha256":"b515815838e4fdbc920983e9425423cd9b8ae3cebf16d4a1cf30aef07aa15fab","abstract_canon_sha256":"df408a5a1c00cb5ed3e3847ebfdea281acbfdc792e134ed0508832480f995362"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:49.345620Z","signature_b64":"NpaVa5ARDflJw1lUpxUOQlwDMw4wn2VgneX3tox+pBucHEpBSWQJ0beRPAXyaTwYa2GMDQTr7DxxxydFzSFmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60d174623af1ec55d0b12282d5f783432855c94695eab0f3d39dd245ff04c06f","last_reissued_at":"2026-05-18T03:46:49.345003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:49.345003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Pellegrino, G. A. Mu\\~noz-Fern\\'andez, J. B. Seoane-Sep\\'ulveda","submitted_at":"2011-07-24T23:52:30Z","abstract_excerpt":"A classical inequality due to H.F. Bohnenblust and E. Hille states that for every positive integer $n$ there is a constant $C_{n}>0$ so that $$(\\sum\\limits_{i_{1},...,i_{n}=1}^{N}|U(e_{i_{^{1}}},...,e_{i_{n}})|^{\\frac{2n}{n+1}})^{\\frac{n+1}{2n}}\\leq C_{n}||U||$$ for every positive integer $N$ and every $n$-linear mapping $U:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow\\mathbb{C}$. The original estimates for those constants from Bohnenblust and Hille are $$C_{n}=n^{\\frac{n+1}{2n}}2^{\\frac{n-1}{2}}.$$ In this note we present explicit formulae for quite better constants, and calcul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4814","kind":"arxiv","version":1},"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":"1107.4814","created_at":"2026-05-18T03:46:49.345098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4814v1","created_at":"2026-05-18T03:46:49.345098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4814","created_at":"2026-05-18T03:46:49.345098+00:00"},{"alias_kind":"pith_short_12","alias_value":"MDIXIYR26HWF","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MDIXIYR26HWFLUFR","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MDIXIYR2","created_at":"2026-05-18T12:26:34.985390+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/MDIXIYR26HWFLUFREKBNL54DIM","json":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM.json","graph_json":"https://pith.science/api/pith-number/MDIXIYR26HWFLUFREKBNL54DIM/graph.json","events_json":"https://pith.science/api/pith-number/MDIXIYR26HWFLUFREKBNL54DIM/events.json","paper":"https://pith.science/paper/MDIXIYR2"},"agent_actions":{"view_html":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM","download_json":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM.json","view_paper":"https://pith.science/paper/MDIXIYR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4814&json=true","fetch_graph":"https://pith.science/api/pith-number/MDIXIYR26HWFLUFREKBNL54DIM/graph.json","fetch_events":"https://pith.science/api/pith-number/MDIXIYR26HWFLUFREKBNL54DIM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM/action/storage_attestation","attest_author":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM/action/author_attestation","sign_citation":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM/action/citation_signature","submit_replication":"https://pith.science/pith/MDIXIYR26HWFLUFREKBNL54DIM/action/replication_record"}},"created_at":"2026-05-18T03:46:49.345098+00:00","updated_at":"2026-05-18T03:46:49.345098+00:00"}