{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UAJMYOAS3XKVUKHQGLKPGTCN4X","short_pith_number":"pith:UAJMYOAS","canonical_record":{"source":{"id":"1709.04552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T22:02:30Z","cross_cats_sorted":[],"title_canon_sha256":"f33dc29672b7afca0c6f8f80dcc2a71023dae227d1a38e372b49037c568efb58","abstract_canon_sha256":"88617d78b119e77a2597aeabfba01d00ca2811ebae0a7f3e81eca1d080a84114"},"schema_version":"1.0"},"canonical_sha256":"a012cc3812ddd55a28f032d4f34c4de5c3359be723bde06c4e2ad6309acb2cb4","source":{"kind":"arxiv","id":"1709.04552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04552","created_at":"2026-05-18T00:35:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04552v1","created_at":"2026-05-18T00:35:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04552","created_at":"2026-05-18T00:35:11Z"},{"alias_kind":"pith_short_12","alias_value":"UAJMYOAS3XKV","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAJMYOAS3XKVUKHQ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAJMYOAS","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UAJMYOAS3XKVUKHQGLKPGTCN4X","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T22:02:30Z","cross_cats_sorted":[],"title_canon_sha256":"f33dc29672b7afca0c6f8f80dcc2a71023dae227d1a38e372b49037c568efb58","abstract_canon_sha256":"88617d78b119e77a2597aeabfba01d00ca2811ebae0a7f3e81eca1d080a84114"},"schema_version":"1.0"},"canonical_sha256":"a012cc3812ddd55a28f032d4f34c4de5c3359be723bde06c4e2ad6309acb2cb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:11.305725Z","signature_b64":"pAGS4rYY4S0UmuGjK+FKNcNNr40mrA7eDIaDkaYh5pvOFSzU6w4WeiPziSQRe3wPEyuEuR2Nz9F02wqskRuBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a012cc3812ddd55a28f032d4f34c4de5c3359be723bde06c4e2ad6309acb2cb4","last_reissued_at":"2026-05-18T00:35:11.305236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:11.305236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04552","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":"2026-05-18T00:35:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hzARvvu1KOwC/A/bjfWj4Axxlcf03due0xil6nGh0l/pKMf/nn0h3C6yrqlR+rrUeNwYtlafR2WgVf6dP/BBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:07:24.709853Z"},"content_sha256":"fd91556e6bfb6f14900d36c250c36bad976ee637198b7424197694ce6fe2b84b","schema_version":"1.0","event_id":"sha256:fd91556e6bfb6f14900d36c250c36bad976ee637198b7424197694ce6fe2b84b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UAJMYOAS3XKVUKHQGLKPGTCN4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Calder\\'{o}n-Zygmund structure of Petermichl's kernel. Weighted inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hugo Aimar, Ivana G\\'omez","submitted_at":"2017-09-13T22:02:30Z","abstract_excerpt":"We show that Petermichl's dyadic operator $\\mathcal{P}$ (S. Petermichl (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol) is a Calder\\'{o}n-Zygmund type operator on an adequate metric normal space of homogeneous type. As a consequence of a general result on spaces of homogeneous type, we get weighted boundedness of the maximal operator $\\mathcal{P}^*$ of truncations of the singular integral. We show that dyadic $A_p$ weights are the good weights for the maximal operator $\\mathcal{P}^*$ of the scale truncations of $\\mathcal{P}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04552","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":"2026-05-18T00:35:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZHEhsYahajvrs0yBqLb1H1QNwBkgIcSsc10oJa5zOZteW340JKPvgSOQYpbWp4h2dYFFNFU7GZehMvrW3kzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:07:24.710248Z"},"content_sha256":"21d730028617012cc57aedfcc8ad2f5f493d386111bb056902c5631328c4ac0f","schema_version":"1.0","event_id":"sha256:21d730028617012cc57aedfcc8ad2f5f493d386111bb056902c5631328c4ac0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X/bundle.json","state_url":"https://pith.science/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X/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":"2026-06-11T09:07:24Z","links":{"resolver":"https://pith.science/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X","bundle":"https://pith.science/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X/bundle.json","state":"https://pith.science/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAJMYOAS3XKVUKHQGLKPGTCN4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UAJMYOAS3XKVUKHQGLKPGTCN4X","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":"88617d78b119e77a2597aeabfba01d00ca2811ebae0a7f3e81eca1d080a84114","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T22:02:30Z","title_canon_sha256":"f33dc29672b7afca0c6f8f80dcc2a71023dae227d1a38e372b49037c568efb58"},"schema_version":"1.0","source":{"id":"1709.04552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04552","created_at":"2026-05-18T00:35:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04552v1","created_at":"2026-05-18T00:35:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04552","created_at":"2026-05-18T00:35:11Z"},{"alias_kind":"pith_short_12","alias_value":"UAJMYOAS3XKV","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAJMYOAS3XKVUKHQ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAJMYOAS","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:21d730028617012cc57aedfcc8ad2f5f493d386111bb056902c5631328c4ac0f","target":"graph","created_at":"2026-05-18T00:35:11Z","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":"We show that Petermichl's dyadic operator $\\mathcal{P}$ (S. Petermichl (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol) is a Calder\\'{o}n-Zygmund type operator on an adequate metric normal space of homogeneous type. As a consequence of a general result on spaces of homogeneous type, we get weighted boundedness of the maximal operator $\\mathcal{P}^*$ of truncations of the singular integral. We show that dyadic $A_p$ weights are the good weights for the maximal operator $\\mathcal{P}^*$ of the scale truncations of $\\mathcal{P}$.","authors_text":"Hugo Aimar, Ivana G\\'omez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T22:02:30Z","title":"On the Calder\\'{o}n-Zygmund structure of Petermichl's kernel. Weighted inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04552","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:fd91556e6bfb6f14900d36c250c36bad976ee637198b7424197694ce6fe2b84b","target":"record","created_at":"2026-05-18T00:35:11Z","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":"88617d78b119e77a2597aeabfba01d00ca2811ebae0a7f3e81eca1d080a84114","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T22:02:30Z","title_canon_sha256":"f33dc29672b7afca0c6f8f80dcc2a71023dae227d1a38e372b49037c568efb58"},"schema_version":"1.0","source":{"id":"1709.04552","kind":"arxiv","version":1}},"canonical_sha256":"a012cc3812ddd55a28f032d4f34c4de5c3359be723bde06c4e2ad6309acb2cb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a012cc3812ddd55a28f032d4f34c4de5c3359be723bde06c4e2ad6309acb2cb4","first_computed_at":"2026-05-18T00:35:11.305236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:11.305236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pAGS4rYY4S0UmuGjK+FKNcNNr40mrA7eDIaDkaYh5pvOFSzU6w4WeiPziSQRe3wPEyuEuR2Nz9F02wqskRuBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:11.305725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd91556e6bfb6f14900d36c250c36bad976ee637198b7424197694ce6fe2b84b","sha256:21d730028617012cc57aedfcc8ad2f5f493d386111bb056902c5631328c4ac0f"],"state_sha256":"3f95a21058ffb57c1d29ea73093042332ba9dc9c0e72a16d1e0559361da9f109"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uIQZbIuFU81aTX0pBtoh1Q0f6ldEhizBzL5PuQFWojNztwQJF5NuDRw+dl/FmfIowi/GQLAR5hFCYXTyd8KBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:07:24.712206Z","bundle_sha256":"2b293aa23058ccb87e0b3e5128c3876888a8acbf621e8fa02a0b6759b16e6227"}}