{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4PPXM6ZJ7QM5QHG4P7N7ZXUE67","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":"ff3c6fbf1fa30a8ac0767ca3f596266e46c0e022f27c7ff561f8eb1506ed8c53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-17T18:31:11Z","title_canon_sha256":"cfb235e9e40e7a80890e09f1b98a36fcd78d53a7296ed16a075d5bc1da7ffcd1"},"schema_version":"1.0","source":{"id":"1110.3756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3756","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3756v2","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3756","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"4PPXM6ZJ7QM5","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4PPXM6ZJ7QM5QHG4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4PPXM6ZJ","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:8610f3dd27d2b8d9253f8eb00368c582e9b2fa3c0a99d98708fa3207d82a568d","target":"graph","created_at":"2026-05-18T03:13:11Z","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":"In connection with proving the A_2 conjecture in 2010, T. Hyt\\\"onen obtained a representation of general Cald\\'eron-Zygmund operators in terms of simpler operators known as Haar shifts. In this note, we prove that the result is sharp in the sense that Haar shift representations of Hyt\\\"onen's type are only available for Calder\\'on-Zygmund operators.","authors_text":"Tuomas Orponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-17T18:31:11Z","title":"On the Haar Shift representations of Calder\\'on-Zygmund Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3756","kind":"arxiv","version":2},"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:d52f632e8da7a45138655a90219fe5e4907277620f013ed9ba4bb2971075d903","target":"record","created_at":"2026-05-18T03:13:11Z","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":"ff3c6fbf1fa30a8ac0767ca3f596266e46c0e022f27c7ff561f8eb1506ed8c53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-17T18:31:11Z","title_canon_sha256":"cfb235e9e40e7a80890e09f1b98a36fcd78d53a7296ed16a075d5bc1da7ffcd1"},"schema_version":"1.0","source":{"id":"1110.3756","kind":"arxiv","version":2}},"canonical_sha256":"e3df767b29fc19d81cdc7fdbfcde84f7e0608870c3554b1aa2581593ec30c2d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3df767b29fc19d81cdc7fdbfcde84f7e0608870c3554b1aa2581593ec30c2d1","first_computed_at":"2026-05-18T03:13:11.079948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:11.079948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9PreFDUvb2st399xXFTlrQiizPItSLRpuD9jI8ixmUyaOKMqGcbD3KrR8wwJ+q1FF22kcCRXsdK2BTMDOZ+gDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:11.080857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d52f632e8da7a45138655a90219fe5e4907277620f013ed9ba4bb2971075d903","sha256:8610f3dd27d2b8d9253f8eb00368c582e9b2fa3c0a99d98708fa3207d82a568d"],"state_sha256":"00561ec9b030d263bb2345b41386e18ca35566e1a0031ba2541bb801ca5ccd03"}