{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7TN3DJHAMT36K5ZE6BHMDJJ3HO","short_pith_number":"pith:7TN3DJHA","schema_version":"1.0","canonical_sha256":"fcdbb1a4e064f7e57724f04ec1a53b3ba71272f4c1f979396a1bef00c5493793","source":{"kind":"arxiv","id":"1207.5375","version":2},"attestation_state":"computed","paper":{"title":"Pisier's inequality revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Assaf Naor, Tuomas Hyt\\\"onen","submitted_at":"2012-07-23T12:55:21Z","abstract_excerpt":"Given a Banach space $X$, for $n\\in \\mathbb N$ and $p\\in (1,\\infty)$ we investigate the smallest constant $\\mathfrak P\\in (0,\\infty)$ for which every $f_1,...,f_n:{-1,1}^n\\to X$ satisfy \\int_{{-1,1}^n}\\Bigg|\\sum_{j=1}^n \\partial_jf_j(\\varepsilon)\\Bigg|^pd\\mu(\\varepsilon) \\leq \\mathfrak{P}^p\\int_{{-1,1}^n}\\int_{{-1,1}^n}\\Bigg\\|\\sum_{j=1}^n \\d_j\\Delta f_j(\\varepsilon)\\Bigg\\|^pd\\mu(\\varepsilon) d\\mu(\\delta), where $\\mu$ is the uniform probability measure on the discrete hypercube ${-1,1}^n$ and ${\\partial_j}_{j=1}^n$ and $\\Delta=\\sum_{j=1}^n\\partial_j$ are the hypercube partial derivatives and th"},"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":"1207.5375","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-23T12:55:21Z","cross_cats_sorted":[],"title_canon_sha256":"fc3f6d092662c4fdbe0ce184b8ee07e869de473deb13c8bf80ebf510e5aea7fc","abstract_canon_sha256":"15a3ac5f6cf83b21c9654479b028ef20bf502044ec26218ca8219b4dbbb6d6e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:46.466099Z","signature_b64":"qSPaNNVzD2Op1+6lMY3Hd8HMIahSk9CsBsKKcoDptOTvEiN5kHLOcEF9HqFwhazP7w2ctrC2EbncXn1QiZyFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcdbb1a4e064f7e57724f04ec1a53b3ba71272f4c1f979396a1bef00c5493793","last_reissued_at":"2026-05-18T03:25:46.465208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:46.465208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pisier's inequality revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Assaf Naor, Tuomas Hyt\\\"onen","submitted_at":"2012-07-23T12:55:21Z","abstract_excerpt":"Given a Banach space $X$, for $n\\in \\mathbb N$ and $p\\in (1,\\infty)$ we investigate the smallest constant $\\mathfrak P\\in (0,\\infty)$ for which every $f_1,...,f_n:{-1,1}^n\\to X$ satisfy \\int_{{-1,1}^n}\\Bigg|\\sum_{j=1}^n \\partial_jf_j(\\varepsilon)\\Bigg|^pd\\mu(\\varepsilon) \\leq \\mathfrak{P}^p\\int_{{-1,1}^n}\\int_{{-1,1}^n}\\Bigg\\|\\sum_{j=1}^n \\d_j\\Delta f_j(\\varepsilon)\\Bigg\\|^pd\\mu(\\varepsilon) d\\mu(\\delta), where $\\mu$ is the uniform probability measure on the discrete hypercube ${-1,1}^n$ and ${\\partial_j}_{j=1}^n$ and $\\Delta=\\sum_{j=1}^n\\partial_j$ are the hypercube partial derivatives and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5375","kind":"arxiv","version":2},"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":"1207.5375","created_at":"2026-05-18T03:25:46.465359+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5375v2","created_at":"2026-05-18T03:25:46.465359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5375","created_at":"2026-05-18T03:25:46.465359+00:00"},{"alias_kind":"pith_short_12","alias_value":"7TN3DJHAMT36","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"7TN3DJHAMT36K5ZE","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"7TN3DJHA","created_at":"2026-05-18T12:26:58.693483+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/7TN3DJHAMT36K5ZE6BHMDJJ3HO","json":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO.json","graph_json":"https://pith.science/api/pith-number/7TN3DJHAMT36K5ZE6BHMDJJ3HO/graph.json","events_json":"https://pith.science/api/pith-number/7TN3DJHAMT36K5ZE6BHMDJJ3HO/events.json","paper":"https://pith.science/paper/7TN3DJHA"},"agent_actions":{"view_html":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO","download_json":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO.json","view_paper":"https://pith.science/paper/7TN3DJHA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5375&json=true","fetch_graph":"https://pith.science/api/pith-number/7TN3DJHAMT36K5ZE6BHMDJJ3HO/graph.json","fetch_events":"https://pith.science/api/pith-number/7TN3DJHAMT36K5ZE6BHMDJJ3HO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO/action/storage_attestation","attest_author":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO/action/author_attestation","sign_citation":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO/action/citation_signature","submit_replication":"https://pith.science/pith/7TN3DJHAMT36K5ZE6BHMDJJ3HO/action/replication_record"}},"created_at":"2026-05-18T03:25:46.465359+00:00","updated_at":"2026-05-18T03:25:46.465359+00:00"}