{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EU4BKK6TMT2PRHZ472UDYOWF7T","short_pith_number":"pith:EU4BKK6T","schema_version":"1.0","canonical_sha256":"2538152bd364f4f89f3cfea83c3ac5fce827dd4c2d524b7270b5ebbf287bb16f","source":{"kind":"arxiv","id":"1612.03958","version":1},"attestation_state":"computed","paper":{"title":"On weak weighted estimates of martingale transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Alexander Reznikov, Alexander Volberg, Fedor Nazarov, Vasily Vasyunin","submitted_at":"2016-12-12T22:42:20Z","abstract_excerpt":"We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture of Muckenhoupt, which stayed open after Muckenhoupt--Wheeden's conjecture was disproved by Reguera--Thiele."},"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":"1612.03958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-12T22:42:20Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"d461fde3e1726a67c6effd5fc87069123d232914864a993c2311e4bc7032384c","abstract_canon_sha256":"f55d6aed285f43ae6da316576b2c2329e3fce0c8773d63edff4d42f688114d28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:32.901198Z","signature_b64":"02DpDjZ8yVjmcOd9rqFeUTWNYtgRN9OTqaGwHuNNOyHyKBVpdXu/xaKYC8gCt9MBvTinQ7vLT0JNvi1CO7QKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2538152bd364f4f89f3cfea83c3ac5fce827dd4c2d524b7270b5ebbf287bb16f","last_reissued_at":"2026-05-18T00:13:32.900707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:32.900707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On weak weighted estimates of martingale transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Alexander Reznikov, Alexander Volberg, Fedor Nazarov, Vasily Vasyunin","submitted_at":"2016-12-12T22:42:20Z","abstract_excerpt":"We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture of Muckenhoupt, which stayed open after Muckenhoupt--Wheeden's conjecture was disproved by Reguera--Thiele."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03958","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":"1612.03958","created_at":"2026-05-18T00:13:32.900793+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.03958v1","created_at":"2026-05-18T00:13:32.900793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03958","created_at":"2026-05-18T00:13:32.900793+00:00"},{"alias_kind":"pith_short_12","alias_value":"EU4BKK6TMT2P","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"EU4BKK6TMT2PRHZ4","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"EU4BKK6T","created_at":"2026-05-18T12:30:15.759754+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/EU4BKK6TMT2PRHZ472UDYOWF7T","json":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T.json","graph_json":"https://pith.science/api/pith-number/EU4BKK6TMT2PRHZ472UDYOWF7T/graph.json","events_json":"https://pith.science/api/pith-number/EU4BKK6TMT2PRHZ472UDYOWF7T/events.json","paper":"https://pith.science/paper/EU4BKK6T"},"agent_actions":{"view_html":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T","download_json":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T.json","view_paper":"https://pith.science/paper/EU4BKK6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.03958&json=true","fetch_graph":"https://pith.science/api/pith-number/EU4BKK6TMT2PRHZ472UDYOWF7T/graph.json","fetch_events":"https://pith.science/api/pith-number/EU4BKK6TMT2PRHZ472UDYOWF7T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T/action/storage_attestation","attest_author":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T/action/author_attestation","sign_citation":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T/action/citation_signature","submit_replication":"https://pith.science/pith/EU4BKK6TMT2PRHZ472UDYOWF7T/action/replication_record"}},"created_at":"2026-05-18T00:13:32.900793+00:00","updated_at":"2026-05-18T00:13:32.900793+00:00"}