{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7Q3U6VXCF2MG33EU5AHJLYL2AI","short_pith_number":"pith:7Q3U6VXC","schema_version":"1.0","canonical_sha256":"fc374f56e22e986dec94e80e95e17a022863e5d9d120904da23f43cada7a0863","source":{"kind":"arxiv","id":"1002.2314","version":3},"attestation_state":"computed","paper":{"title":"On Burkholder function for orthogonal martingales and zeros of Legendre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alexander Borichev, Alexander Volberg, Prabhu Janakiraman","submitted_at":"2010-02-11T10:24:19Z","abstract_excerpt":"Burkholder obtained a sharp estimate of $\\E|W|^p$ via $\\E|Z|^p$, where $W$ is a martingale transform of $Z$, or, in other words, for martingales $W$ differentially subordinated to martingales $Z$. His result is that $\\E|W|^p\\le (p^*-1)^p\\E|Z|^p$, where $p^* =\\max (p, \\frac{p}{p-1})$. What happens if the martingales have an extra property of being orthogonal martingales? This property is an analog (for martingales) of the Cauchy-Riemann equation for functions, and it naturally appears from a problem on singular integrals (see the references at the end of Section~1). We establish here that in 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":"1002.2314","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-11T10:24:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"95720a671ea58ac89b5edf3d7f022dd1bf9afd04b9baaa33506261e316b45376","abstract_canon_sha256":"3cc77756251b331e0beba89b5c99ac37416aa8b3bcc8c3963350b406f9d81638"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:29.035581Z","signature_b64":"RumSYeRBBjM7Hh/WWXIP9liaqh/jql/axMel5wRacKdYR4TIQbURgmczlbyE5ZKeLZ5dpIdgVaZxAxbm8+ziCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc374f56e22e986dec94e80e95e17a022863e5d9d120904da23f43cada7a0863","last_reissued_at":"2026-05-18T04:11:29.035039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:29.035039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Burkholder function for orthogonal martingales and zeros of Legendre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alexander Borichev, Alexander Volberg, Prabhu Janakiraman","submitted_at":"2010-02-11T10:24:19Z","abstract_excerpt":"Burkholder obtained a sharp estimate of $\\E|W|^p$ via $\\E|Z|^p$, where $W$ is a martingale transform of $Z$, or, in other words, for martingales $W$ differentially subordinated to martingales $Z$. His result is that $\\E|W|^p\\le (p^*-1)^p\\E|Z|^p$, where $p^* =\\max (p, \\frac{p}{p-1})$. What happens if the martingales have an extra property of being orthogonal martingales? This property is an analog (for martingales) of the Cauchy-Riemann equation for functions, and it naturally appears from a problem on singular integrals (see the references at the end of Section~1). We establish here that in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2314","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":"1002.2314","created_at":"2026-05-18T04:11:29.035120+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.2314v3","created_at":"2026-05-18T04:11:29.035120+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2314","created_at":"2026-05-18T04:11:29.035120+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Q3U6VXCF2MG","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Q3U6VXCF2MG33EU","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Q3U6VXC","created_at":"2026-05-18T12:26:05.355336+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/7Q3U6VXCF2MG33EU5AHJLYL2AI","json":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI.json","graph_json":"https://pith.science/api/pith-number/7Q3U6VXCF2MG33EU5AHJLYL2AI/graph.json","events_json":"https://pith.science/api/pith-number/7Q3U6VXCF2MG33EU5AHJLYL2AI/events.json","paper":"https://pith.science/paper/7Q3U6VXC"},"agent_actions":{"view_html":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI","download_json":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI.json","view_paper":"https://pith.science/paper/7Q3U6VXC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.2314&json=true","fetch_graph":"https://pith.science/api/pith-number/7Q3U6VXCF2MG33EU5AHJLYL2AI/graph.json","fetch_events":"https://pith.science/api/pith-number/7Q3U6VXCF2MG33EU5AHJLYL2AI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI/action/storage_attestation","attest_author":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI/action/author_attestation","sign_citation":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI/action/citation_signature","submit_replication":"https://pith.science/pith/7Q3U6VXCF2MG33EU5AHJLYL2AI/action/replication_record"}},"created_at":"2026-05-18T04:11:29.035120+00:00","updated_at":"2026-05-18T04:11:29.035120+00:00"}