{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XIIDVR2QNILUDHU4XY7BD6O535","short_pith_number":"pith:XIIDVR2Q","canonical_record":{"source":{"id":"1803.01046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-02T21:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"11fef73114cd4e8e76880e875205e338d4b9147af9c6f5393b201029773540ca","abstract_canon_sha256":"4218fece2ed7162c0199b4f40c5f5d80b7ef339ac9ea01206efc40822778414e"},"schema_version":"1.0"},"canonical_sha256":"ba103ac7506a17419e9cbe3e11f9dddf706e1356010bc6dde81c9ba915f48eca","source":{"kind":"arxiv","id":"1803.01046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01046","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01046v1","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01046","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"XIIDVR2QNILU","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XIIDVR2QNILUDHU4","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XIIDVR2Q","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XIIDVR2QNILUDHU4XY7BD6O535","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-02T21:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"11fef73114cd4e8e76880e875205e338d4b9147af9c6f5393b201029773540ca","abstract_canon_sha256":"4218fece2ed7162c0199b4f40c5f5d80b7ef339ac9ea01206efc40822778414e"},"schema_version":"1.0"},"canonical_sha256":"ba103ac7506a17419e9cbe3e11f9dddf706e1356010bc6dde81c9ba915f48eca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:01.916844Z","signature_b64":"kZakdMTigSrQKjSzkmL1Qtm8DKIMbDV6rG/7WvOObibNqQfKHHabPoPImS6r6/pB0qwuG/Pz4TG8PheMfpRsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba103ac7506a17419e9cbe3e11f9dddf706e1356010bc6dde81c9ba915f48eca","last_reissued_at":"2026-05-18T00:22:01.916231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:01.916231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01046","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xj1VF43wbiu+XEsxAIhm0QdCA+EDr1UZd7qbX4pp2FOn4yHmZqy2ymuvHFVfFY6O/9MKdmj6fp1l1w/PTB38CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:24:04.857265Z"},"content_sha256":"45bbcf86ec7159caa512f38e5bd26c609f2bccf9a102fe13d9b81abbb0032602","schema_version":"1.0","event_id":"sha256:45bbcf86ec7159caa512f38e5bd26c609f2bccf9a102fe13d9b81abbb0032602"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XIIDVR2QNILUDHU4XY7BD6O535","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Class of Multiparameter Oscillatory Singular Integral Operators: Endpoint Hardy Space Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Diana Cristina Rinc\\'on Mart\\'inez, Eric Latorre, James Wright, Odysseas Bakas","submitted_at":"2018-03-02T21:23:57Z","abstract_excerpt":"We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\\'e-type covering lemma to deduce bounds on product $H^1$ is not valid.\n  We consider the class of multiparameter oscillatory singular integral operators given by convolution with the classical multiple Hilbert transform kernel modulated by a general polynomial oscillation. Various characterisations are known which give $L^2$ (or more generally $L^p, 1<p<\\infty$) bounds. Here we i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01046","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUVEx0R/vTecBWZvNJImR+1HKltB+Kpy+wK4op/NTGhiGQwdCTFuDDLQqQVTHf8sCyK0XcvoigrLwZR0Yu4cAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:24:04.858037Z"},"content_sha256":"32d944cb113d555830765741784cb1aa499fa1921f88c646ff71a7d5e9a43d2f","schema_version":"1.0","event_id":"sha256:32d944cb113d555830765741784cb1aa499fa1921f88c646ff71a7d5e9a43d2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XIIDVR2QNILUDHU4XY7BD6O535/bundle.json","state_url":"https://pith.science/pith/XIIDVR2QNILUDHU4XY7BD6O535/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XIIDVR2QNILUDHU4XY7BD6O535/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T07:24:04Z","links":{"resolver":"https://pith.science/pith/XIIDVR2QNILUDHU4XY7BD6O535","bundle":"https://pith.science/pith/XIIDVR2QNILUDHU4XY7BD6O535/bundle.json","state":"https://pith.science/pith/XIIDVR2QNILUDHU4XY7BD6O535/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XIIDVR2QNILUDHU4XY7BD6O535/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XIIDVR2QNILUDHU4XY7BD6O535","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":"4218fece2ed7162c0199b4f40c5f5d80b7ef339ac9ea01206efc40822778414e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-02T21:23:57Z","title_canon_sha256":"11fef73114cd4e8e76880e875205e338d4b9147af9c6f5393b201029773540ca"},"schema_version":"1.0","source":{"id":"1803.01046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01046","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01046v1","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01046","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"XIIDVR2QNILU","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XIIDVR2QNILUDHU4","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XIIDVR2Q","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:32d944cb113d555830765741784cb1aa499fa1921f88c646ff71a7d5e9a43d2f","target":"graph","created_at":"2026-05-18T00:22:01Z","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":"We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\\'e-type covering lemma to deduce bounds on product $H^1$ is not valid.\n  We consider the class of multiparameter oscillatory singular integral operators given by convolution with the classical multiple Hilbert transform kernel modulated by a general polynomial oscillation. Various characterisations are known which give $L^2$ (or more generally $L^p, 1<p<\\infty$) bounds. Here we i","authors_text":"Diana Cristina Rinc\\'on Mart\\'inez, Eric Latorre, James Wright, Odysseas Bakas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-02T21:23:57Z","title":"A Class of Multiparameter Oscillatory Singular Integral Operators: Endpoint Hardy Space Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01046","kind":"arxiv","version":1},"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":"sha256:45bbcf86ec7159caa512f38e5bd26c609f2bccf9a102fe13d9b81abbb0032602","target":"record","created_at":"2026-05-18T00:22:01Z","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":"4218fece2ed7162c0199b4f40c5f5d80b7ef339ac9ea01206efc40822778414e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-02T21:23:57Z","title_canon_sha256":"11fef73114cd4e8e76880e875205e338d4b9147af9c6f5393b201029773540ca"},"schema_version":"1.0","source":{"id":"1803.01046","kind":"arxiv","version":1}},"canonical_sha256":"ba103ac7506a17419e9cbe3e11f9dddf706e1356010bc6dde81c9ba915f48eca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba103ac7506a17419e9cbe3e11f9dddf706e1356010bc6dde81c9ba915f48eca","first_computed_at":"2026-05-18T00:22:01.916231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:01.916231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZakdMTigSrQKjSzkmL1Qtm8DKIMbDV6rG/7WvOObibNqQfKHHabPoPImS6r6/pB0qwuG/Pz4TG8PheMfpRsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:01.916844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45bbcf86ec7159caa512f38e5bd26c609f2bccf9a102fe13d9b81abbb0032602","sha256:32d944cb113d555830765741784cb1aa499fa1921f88c646ff71a7d5e9a43d2f"],"state_sha256":"86db35cc6c4038c2a8594d4c07f75169457260baa58ba4ca4f03a43213ba37ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3naMD/STnFHaokhyxWChlTjIg0K6U3Y6Z0fdggrnm6APQgNQLXNqEpY8kCVkF51TtN9+wHJJyCzb9r8VOMKoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T07:24:04.861844Z","bundle_sha256":"df42595011856566090c76972368fd5d142cba67b420801d93bc50455379846c"}}