{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A4NGXIRZHK3ZIMFNU2RJBS4MT2","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":"d763eae5fdfede0c05a029f6796e6aa594808a252b89b330cd87a03184988fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-22T07:12:45Z","title_canon_sha256":"7e109268c5abc4ddf3997ca2a52059e39f9cccb502dfd6828e56f63662cff1af"},"schema_version":"1.0","source":{"id":"1211.5218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5218","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5218v2","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5218","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"A4NGXIRZHK3Z","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A4NGXIRZHK3ZIMFN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A4NGXIRZ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:85c32600fc5c6aaea6979c4ad9836863e35c5095067ae2b11bf93884768ec1bc","target":"graph","created_at":"2026-05-18T03:26:42Z","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 this work, we describe several results exhibited during a talk at the El Escorial 2012 conference. We aim to pursue the development of a multi-frequency Calderon-Zygmund analysis introduced in [9]. We set a definition of general multi-frequency Calderon-Zygmund operator. Unweighted estimates are obtained using the corresponding multi-frequency decomposition of [9]. Involving a new kind of maximal sharp function, weighted estimates are obtained.","authors_text":"Frederic Bernicot (LMJL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-22T07:12:45Z","title":"Multi-frequency Calderon-Zygmund analysis and connexion to Bochner-Riesz multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5218","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:f258dd1fa27318a9ac054b8d4377d5f71f5d5aaf63115f48ae619f00d52682b1","target":"record","created_at":"2026-05-18T03:26:42Z","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":"d763eae5fdfede0c05a029f6796e6aa594808a252b89b330cd87a03184988fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-22T07:12:45Z","title_canon_sha256":"7e109268c5abc4ddf3997ca2a52059e39f9cccb502dfd6828e56f63662cff1af"},"schema_version":"1.0","source":{"id":"1211.5218","kind":"arxiv","version":2}},"canonical_sha256":"071a6ba2393ab79430ada6a290cb8c9e863be94abadc696b429f8091a3614002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"071a6ba2393ab79430ada6a290cb8c9e863be94abadc696b429f8091a3614002","first_computed_at":"2026-05-18T03:26:42.685704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:42.685704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1w3BBr0PFXlHsJ84k9SbXOfqJWZrj2Nb3xXuGNM3wBp5zhJaiYNFnlkhPiA0Ku5GjR78vP5LMSJvrv0AuM9NAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:42.686205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f258dd1fa27318a9ac054b8d4377d5f71f5d5aaf63115f48ae619f00d52682b1","sha256:85c32600fc5c6aaea6979c4ad9836863e35c5095067ae2b11bf93884768ec1bc"],"state_sha256":"98228f8fbdab5e0ab6137121e285ac51c5adf2d54f1357373742861d3332d638"}