{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YU4UU2HI7E7MPPH3YFMFPWXPBC","short_pith_number":"pith:YU4UU2HI","schema_version":"1.0","canonical_sha256":"c5394a68e8f93ec7bcfbc15857daef0884073e24c8531779cee12d17ae8fe050","source":{"kind":"arxiv","id":"1706.01930","version":2},"attestation_state":"computed","paper":{"title":"Square functions and the Hamming cube: Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Fedor Nazarov, Paata Ivanisvili","submitted_at":"2017-06-06T18:59:36Z","abstract_excerpt":"For $1<p\\leq 2$, any $n\\geq 1$ and any $f:\\{-1,1\\}^{n} \\to \\mathbb{R}$, we obtain $(\\mathbb{E} |\\nabla f|^{p})^{1/p} \\geq C(p)(\\mathbb{E}|f|^{p} - |\\mathbb{E}f|^{p})^{1/p}$ where $C(p)$ is the smallest positive zero of the confluent hypergeometric function ${}_{1}F_{1}(\\frac{p}{2(1-p)}, \\frac{1}{2}, \\frac{x^{2}}{2})$. Our approach is based on a certain duality between the classical square function estimates on the Euclidean space and the gradient estimates on the Hamming cube."},"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":"1706.01930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-06T18:59:36Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7836b318f11b98d79a21232256a168ef08d24c7f9ab87ec4564019ff4a12e09d","abstract_canon_sha256":"1b4a3b36ff783baae2b6ee6df83a43ebbd99d2502fc45a2d0818e309930b372e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:39.431021Z","signature_b64":"wogYbdTGf7VTrmPWEhQEtvdWP1bDibm6zH8LgwCqrRGuA7VZ60C5lYfNOc7FquDwTe3qPMGTh3dUlJwVgwoJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5394a68e8f93ec7bcfbc15857daef0884073e24c8531779cee12d17ae8fe050","last_reissued_at":"2026-05-18T00:25:39.430255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:39.430255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Square functions and the Hamming cube: Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Fedor Nazarov, Paata Ivanisvili","submitted_at":"2017-06-06T18:59:36Z","abstract_excerpt":"For $1<p\\leq 2$, any $n\\geq 1$ and any $f:\\{-1,1\\}^{n} \\to \\mathbb{R}$, we obtain $(\\mathbb{E} |\\nabla f|^{p})^{1/p} \\geq C(p)(\\mathbb{E}|f|^{p} - |\\mathbb{E}f|^{p})^{1/p}$ where $C(p)$ is the smallest positive zero of the confluent hypergeometric function ${}_{1}F_{1}(\\frac{p}{2(1-p)}, \\frac{1}{2}, \\frac{x^{2}}{2})$. Our approach is based on a certain duality between the classical square function estimates on the Euclidean space and the gradient estimates on the Hamming cube."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01930","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":"1706.01930","created_at":"2026-05-18T00:25:39.430381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01930v2","created_at":"2026-05-18T00:25:39.430381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01930","created_at":"2026-05-18T00:25:39.430381+00:00"},{"alias_kind":"pith_short_12","alias_value":"YU4UU2HI7E7M","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YU4UU2HI7E7MPPH3","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YU4UU2HI","created_at":"2026-05-18T12:31:56.362134+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/YU4UU2HI7E7MPPH3YFMFPWXPBC","json":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC.json","graph_json":"https://pith.science/api/pith-number/YU4UU2HI7E7MPPH3YFMFPWXPBC/graph.json","events_json":"https://pith.science/api/pith-number/YU4UU2HI7E7MPPH3YFMFPWXPBC/events.json","paper":"https://pith.science/paper/YU4UU2HI"},"agent_actions":{"view_html":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC","download_json":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC.json","view_paper":"https://pith.science/paper/YU4UU2HI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01930&json=true","fetch_graph":"https://pith.science/api/pith-number/YU4UU2HI7E7MPPH3YFMFPWXPBC/graph.json","fetch_events":"https://pith.science/api/pith-number/YU4UU2HI7E7MPPH3YFMFPWXPBC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC/action/storage_attestation","attest_author":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC/action/author_attestation","sign_citation":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC/action/citation_signature","submit_replication":"https://pith.science/pith/YU4UU2HI7E7MPPH3YFMFPWXPBC/action/replication_record"}},"created_at":"2026-05-18T00:25:39.430381+00:00","updated_at":"2026-05-18T00:25:39.430381+00:00"}