{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UDELIBX5ZY3DDR6GLKZJAMPFCW","short_pith_number":"pith:UDELIBX5","schema_version":"1.0","canonical_sha256":"a0c8b406fdce3631c7c65ab29031e515bba660b22bf998bc2de77565727312e6","source":{"kind":"arxiv","id":"1608.04021","version":1},"attestation_state":"computed","paper":{"title":"Poincar\\'e inequality 3/2 on the Hamming cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Paata Ivanisvili","submitted_at":"2016-08-13T19:39:23Z","abstract_excerpt":"For any $n \\geq 1$, and any $f :\\{-1,1\\}^{n} \\to \\mathbb{R}$ we have $ \\Re\\, \\mathbb{E}\\, (f + i\\, |\\nabla f|)^{3/2} \\leq \\Re\\, (\\mathbb{E}f)^{3/2}, $ where $z^{3/2}$ for $z=x+iy$ is taken with principal branch and $\\Re$ denotes the real part."},"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":"1608.04021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-13T19:39:23Z","cross_cats_sorted":[],"title_canon_sha256":"6a0f862a656cb5d36f0584a1f9ae184de346ba663662c7262c92e0b5551b970d","abstract_canon_sha256":"2f9d7e91665bde33b7b7642facdb296158e0cdfa2039316f28357bb65ec14a16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:04.441781Z","signature_b64":"V9x1tfZWZNbmrINDpk9oQ9cOt9fK1qF9lVFznL6lkf/0/Gf/ModBXvAe/SshC/BZANmebO/DTXpNe5gHTJbUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0c8b406fdce3631c7c65ab29031e515bba660b22bf998bc2de77565727312e6","last_reissued_at":"2026-05-18T01:09:04.441414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:04.441414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e inequality 3/2 on the Hamming cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Paata Ivanisvili","submitted_at":"2016-08-13T19:39:23Z","abstract_excerpt":"For any $n \\geq 1$, and any $f :\\{-1,1\\}^{n} \\to \\mathbb{R}$ we have $ \\Re\\, \\mathbb{E}\\, (f + i\\, |\\nabla f|)^{3/2} \\leq \\Re\\, (\\mathbb{E}f)^{3/2}, $ where $z^{3/2}$ for $z=x+iy$ is taken with principal branch and $\\Re$ denotes the real part."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04021","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":"1608.04021","created_at":"2026-05-18T01:09:04.441478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.04021v1","created_at":"2026-05-18T01:09:04.441478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04021","created_at":"2026-05-18T01:09:04.441478+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDELIBX5ZY3D","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDELIBX5ZY3DDR6G","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDELIBX5","created_at":"2026-05-18T12:30:46.583412+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/UDELIBX5ZY3DDR6GLKZJAMPFCW","json":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW.json","graph_json":"https://pith.science/api/pith-number/UDELIBX5ZY3DDR6GLKZJAMPFCW/graph.json","events_json":"https://pith.science/api/pith-number/UDELIBX5ZY3DDR6GLKZJAMPFCW/events.json","paper":"https://pith.science/paper/UDELIBX5"},"agent_actions":{"view_html":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW","download_json":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW.json","view_paper":"https://pith.science/paper/UDELIBX5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.04021&json=true","fetch_graph":"https://pith.science/api/pith-number/UDELIBX5ZY3DDR6GLKZJAMPFCW/graph.json","fetch_events":"https://pith.science/api/pith-number/UDELIBX5ZY3DDR6GLKZJAMPFCW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW/action/storage_attestation","attest_author":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW/action/author_attestation","sign_citation":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW/action/citation_signature","submit_replication":"https://pith.science/pith/UDELIBX5ZY3DDR6GLKZJAMPFCW/action/replication_record"}},"created_at":"2026-05-18T01:09:04.441478+00:00","updated_at":"2026-05-18T01:09:04.441478+00:00"}