{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LTMIK72XJEZYB2W3KTNNROAWBR","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":"6a96b51933f27ff8f984080e26d7d8791cbad2f52e9611e1bfe0a62d4150e954","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-10-29T16:41:47Z","title_canon_sha256":"7d092d8ea0511dcd8e4fa4dbf6a363dee1dd17a65e634a50ff8e041ce5551784"},"schema_version":"1.0","source":{"id":"1410.8055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8055","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8055v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8055","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"LTMIK72XJEZY","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LTMIK72XJEZYB2W3","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LTMIK72X","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:cde929e0760beb867b61c078bc7869b8cead0301c04d33c86d369f96d8a2e9c0","target":"graph","created_at":"2026-05-18T02:39:07Z","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 formulate a class of singular integral operators in arbitrarily many parameters using mixed type characterizing conditions. We also prove a multi-parameter representation theorem saying that a general operator in our class can be represented as an average of sums of dyadic shifts, which implies a new multi-parameter $T1$ theorem as a byproduct. Furthermore, an equivalence result between ours and Journ\\'e's class of multi-parameter operators is established, whose proof requires the multi-parameter $T1$ theorem. These results generalize to arbitrarily many parameters recent results of Hyt\\\"on","authors_text":"Yumeng Ou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-10-29T16:41:47Z","title":"Multi-parameter singular integral operators and representation theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8055","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:ff6803ce569cb1acc0b2afadb7467cc1bb4bde8832bdcc6b8f22b64aedb1b6e4","target":"record","created_at":"2026-05-18T02:39:07Z","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":"6a96b51933f27ff8f984080e26d7d8791cbad2f52e9611e1bfe0a62d4150e954","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-10-29T16:41:47Z","title_canon_sha256":"7d092d8ea0511dcd8e4fa4dbf6a363dee1dd17a65e634a50ff8e041ce5551784"},"schema_version":"1.0","source":{"id":"1410.8055","kind":"arxiv","version":1}},"canonical_sha256":"5cd8857f57493380eadb54dad8b8160c685b3bb8e4c9b0faf494646e774afe40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cd8857f57493380eadb54dad8b8160c685b3bb8e4c9b0faf494646e774afe40","first_computed_at":"2026-05-18T02:39:07.419824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:07.419824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E/w7Kr76znzO1awcBTuCLkj7R/9wrm9CEqBWNrQbiwFuqCP0RNyW8T6dHAHCTtIcXOF9HgEsvnZ02aEX85UgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:07.420471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff6803ce569cb1acc0b2afadb7467cc1bb4bde8832bdcc6b8f22b64aedb1b6e4","sha256:cde929e0760beb867b61c078bc7869b8cead0301c04d33c86d369f96d8a2e9c0"],"state_sha256":"a1fc80b126eaff3dbeea918d9afb4538a6addf601accd96019cbe7b841316886"}