{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7Q3U6VXCF2MG33EU5AHJLYL2AI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3cc77756251b331e0beba89b5c99ac37416aa8b3bcc8c3963350b406f9d81638","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-11T10:24:19Z","title_canon_sha256":"95720a671ea58ac89b5edf3d7f022dd1bf9afd04b9baaa33506261e316b45376"},"schema_version":"1.0","source":{"id":"1002.2314","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2314","created_at":"2026-05-18T04:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2314v3","created_at":"2026-05-18T04:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2314","created_at":"2026-05-18T04:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"7Q3U6VXCF2MG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7Q3U6VXCF2MG33EU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7Q3U6VXC","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:2613314087fff009f741587b3edd951d04bfeb9b49cbcacdf1a9e1c353c22e96","target":"graph","created_at":"2026-05-18T04:11:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Alexander Borichev, Alexander Volberg, Prabhu Janakiraman","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-11T10:24:19Z","title":"On Burkholder function for orthogonal martingales and zeros of Legendre polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2314","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:52dc7c0595ef11e791668d33b4d16ea1dc6e0069b68f62874935cb02d9c30875","target":"record","created_at":"2026-05-18T04:11:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3cc77756251b331e0beba89b5c99ac37416aa8b3bcc8c3963350b406f9d81638","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-11T10:24:19Z","title_canon_sha256":"95720a671ea58ac89b5edf3d7f022dd1bf9afd04b9baaa33506261e316b45376"},"schema_version":"1.0","source":{"id":"1002.2314","kind":"arxiv","version":3}},"canonical_sha256":"fc374f56e22e986dec94e80e95e17a022863e5d9d120904da23f43cada7a0863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc374f56e22e986dec94e80e95e17a022863e5d9d120904da23f43cada7a0863","first_computed_at":"2026-05-18T04:11:29.035039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:29.035039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RumSYeRBBjM7Hh/WWXIP9liaqh/jql/axMel5wRacKdYR4TIQbURgmczlbyE5ZKeLZ5dpIdgVaZxAxbm8+ziCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:29.035581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2314","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52dc7c0595ef11e791668d33b4d16ea1dc6e0069b68f62874935cb02d9c30875","sha256:2613314087fff009f741587b3edd951d04bfeb9b49cbcacdf1a9e1c353c22e96"],"state_sha256":"d0369ce02291dc9e6058c344d20b04203a50eb7b565624a643ffbc076147a650"}