{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QPMFHDCTBGCYOMCW3JH6JRJVNZ","short_pith_number":"pith:QPMFHDCT","canonical_record":{"source":{"id":"1202.2229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T10:12:18Z","cross_cats_sorted":[],"title_canon_sha256":"74fe60d4e64a045fc52702dbea660ab03b346cc3ba732802f7d8fa28b04ee8cd","abstract_canon_sha256":"e0f6b7b59d803add371ddc3ba1a643ab9c13f35b0ec2f680c30c76df417c4070"},"schema_version":"1.0"},"canonical_sha256":"83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b","source":{"kind":"arxiv","id":"1202.2229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2229","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2229v1","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2229","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"QPMFHDCTBGCY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPMFHDCTBGCYOMCW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPMFHDCT","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QPMFHDCTBGCYOMCW3JH6JRJVNZ","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T10:12:18Z","cross_cats_sorted":[],"title_canon_sha256":"74fe60d4e64a045fc52702dbea660ab03b346cc3ba732802f7d8fa28b04ee8cd","abstract_canon_sha256":"e0f6b7b59d803add371ddc3ba1a643ab9c13f35b0ec2f680c30c76df417c4070"},"schema_version":"1.0"},"canonical_sha256":"83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:58.926734Z","signature_b64":"IhzljZ0lFdycH0dW/wJsmVSFUj5iXTlBpkEqWWc/cS5Mxtd850f6fQjL6ruYohblGZ7x8tHoAzfOGwNc1hWlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b","last_reissued_at":"2026-05-18T01:33:58.926193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:58.926193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2229","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":"2026-05-18T01:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7ImwosMS7kr9GKvMnPU5MViELiKkMhYBZ6co5S2TkqMn1T9+LVtjq3mcbO1DICfKQvqYUOHqKS0pqIkikS6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:20:52.031835Z"},"content_sha256":"0280fa3fe3c55d6ef4618e34edb241bc9a9e078ceb6a46a5310aca8201b80b5f","schema_version":"1.0","event_id":"sha256:0280fa3fe3c55d6ef4618e34edb241bc9a9e078ceb6a46a5310aca8201b80b5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QPMFHDCTBGCYOMCW3JH6JRJVNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos P\\'erez, Michael T. Lacey, Tuomas P. Hyt\\\"onen","submitted_at":"2012-02-10T10:12:18Z","abstract_excerpt":"Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous results in this direction. Our argument also applies to the q-variation of certain Calderon-Zygmund operators, a stronger nonlinearity than the maximal truncations. As an application, we obtain new sharp weighted inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2229","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":"2026-05-18T01:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kdeovb5wrPKJmHiN/FZV73TgJF5b3dY87vvLWoZAYMgutWySUZlIzQMt3/5T47jyRvxxuUDgZFwx0zSwmcb9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:20:52.032566Z"},"content_sha256":"5464e300191e469becfce0f4941d5fe275be548148ea1ec14fd19493fac002b6","schema_version":"1.0","event_id":"sha256:5464e300191e469becfce0f4941d5fe275be548148ea1ec14fd19493fac002b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ/bundle.json","state_url":"https://pith.science/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ/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":"2026-05-25T21:20:52Z","links":{"resolver":"https://pith.science/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ","bundle":"https://pith.science/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ/bundle.json","state":"https://pith.science/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPMFHDCTBGCYOMCW3JH6JRJVNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QPMFHDCTBGCYOMCW3JH6JRJVNZ","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":"e0f6b7b59d803add371ddc3ba1a643ab9c13f35b0ec2f680c30c76df417c4070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T10:12:18Z","title_canon_sha256":"74fe60d4e64a045fc52702dbea660ab03b346cc3ba732802f7d8fa28b04ee8cd"},"schema_version":"1.0","source":{"id":"1202.2229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2229","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2229v1","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2229","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"QPMFHDCTBGCY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPMFHDCTBGCYOMCW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPMFHDCT","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:5464e300191e469becfce0f4941d5fe275be548148ea1ec14fd19493fac002b6","target":"graph","created_at":"2026-05-18T01:33:58Z","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":"Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous results in this direction. Our argument also applies to the q-variation of certain Calderon-Zygmund operators, a stronger nonlinearity than the maximal truncations. As an application, we obtain new sharp weighted inequalities.","authors_text":"Carlos P\\'erez, Michael T. Lacey, Tuomas P. Hyt\\\"onen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T10:12:18Z","title":"Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2229","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":"sha256:0280fa3fe3c55d6ef4618e34edb241bc9a9e078ceb6a46a5310aca8201b80b5f","target":"record","created_at":"2026-05-18T01:33:58Z","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":"e0f6b7b59d803add371ddc3ba1a643ab9c13f35b0ec2f680c30c76df417c4070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T10:12:18Z","title_canon_sha256":"74fe60d4e64a045fc52702dbea660ab03b346cc3ba732802f7d8fa28b04ee8cd"},"schema_version":"1.0","source":{"id":"1202.2229","kind":"arxiv","version":1}},"canonical_sha256":"83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83d8538c530985873056da4fe4c5356e72bb0c682f9d5819aed48cf5cd8f4b3b","first_computed_at":"2026-05-18T01:33:58.926193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:58.926193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IhzljZ0lFdycH0dW/wJsmVSFUj5iXTlBpkEqWWc/cS5Mxtd850f6fQjL6ruYohblGZ7x8tHoAzfOGwNc1hWlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:58.926734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0280fa3fe3c55d6ef4618e34edb241bc9a9e078ceb6a46a5310aca8201b80b5f","sha256:5464e300191e469becfce0f4941d5fe275be548148ea1ec14fd19493fac002b6"],"state_sha256":"b9fc8d5f65665fe576c2c311b82c045083877cdd488bfb0c622fcc178b012d98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7+KGzo+p4vPnR92fTJVtC1618TSDbnoiVtXXZD75eh8yGNVK2rJ5QgEIk9TD1tXXVJ0q/uI8qBZ8JgP3LQrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:20:52.036367Z","bundle_sha256":"59f1371ff47775ae9bc5ae308685d178786983a15030a494ccbcf722ae93eb1b"}}