{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4MSTKOQDOASQEUML6IUTLO3FVW","short_pith_number":"pith:4MSTKOQD","canonical_record":{"source":{"id":"1311.5175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-20T19:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"8b5bb9c3e99732bde2465453b9c075c32cdfaa7a881504ab98cf34c3c5353723","abstract_canon_sha256":"7396a09729e25d11303ecb9e36b2e945400a4591f725815f21f1170a087eb03b"},"schema_version":"1.0"},"canonical_sha256":"e325353a03702502518bf22935bb65adb6a8a12badc8530820f569f3711f8f62","source":{"kind":"arxiv","id":"1311.5175","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5175","created_at":"2026-05-18T03:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5175v1","created_at":"2026-05-18T03:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5175","created_at":"2026-05-18T03:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"4MSTKOQDOASQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4MSTKOQDOASQEUML","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4MSTKOQD","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4MSTKOQDOASQEUML6IUTLO3FVW","target":"record","payload":{"canonical_record":{"source":{"id":"1311.5175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-20T19:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"8b5bb9c3e99732bde2465453b9c075c32cdfaa7a881504ab98cf34c3c5353723","abstract_canon_sha256":"7396a09729e25d11303ecb9e36b2e945400a4591f725815f21f1170a087eb03b"},"schema_version":"1.0"},"canonical_sha256":"e325353a03702502518bf22935bb65adb6a8a12badc8530820f569f3711f8f62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:35.040638Z","signature_b64":"BemHMV7b1uOgE4iA7tKohKvMR6kWtYUdBS6xZZuk0boPKuIlfXzwxuESihNEQrqTEHd+QTW6bkTfbbPJzhPGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e325353a03702502518bf22935bb65adb6a8a12badc8530820f569f3711f8f62","last_reissued_at":"2026-05-18T03:06:35.039937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:35.039937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.5175","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":"2026-05-18T03:06:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAVVvIQtaTNccG4sxUmXU22lvg7+8CyVrjaF1t2nbPelt6uzmbYye/kPj9bPzB+CKNQ3VllPuMJgTsli3EL4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:10:30.166721Z"},"content_sha256":"8a767e19a8d0301259c96f61b468cd303fefc69b6fb0bf76b5a89f1a29fee6a6","schema_version":"1.0","event_id":"sha256:8a767e19a8d0301259c96f61b468cd303fefc69b6fb0bf76b5a89f1a29fee6a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4MSTKOQDOASQEUML6IUTLO3FVW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cauchy-type integrals in several complex variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Elias M. Stein, Loredana Lanzani","submitted_at":"2013-11-20T19:05:29Z","abstract_excerpt":"We present the theory of Cauchy-Fantappi\\'e integral operators, with emphasis on the situation when the domain of integration, $D$, has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel is a holomorphic function of the parameter $z\\in D$. The goal is to prove $L^p$ estimates for these operators and, as a consequence, to obtain $L^p$ estimates for the canonical Cauchy-Szeg\\\"o and Bergman projection operators (which are not of Cauchy-Fantappi\\'e type)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5175","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":"2026-05-18T03:06:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wF6IDNxhh5PxjrqhlsRO8yQKLhjDTL5Zqm92Iys3HB6aRO2QE7FZ/7frkQJ730HTt9bjuyvKG+deTmxvs+bWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:10:30.167388Z"},"content_sha256":"754b7e43602c48bdfb6e392766d45cee0bd4f98a13ca13e368b3d33dd2446af8","schema_version":"1.0","event_id":"sha256:754b7e43602c48bdfb6e392766d45cee0bd4f98a13ca13e368b3d33dd2446af8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MSTKOQDOASQEUML6IUTLO3FVW/bundle.json","state_url":"https://pith.science/pith/4MSTKOQDOASQEUML6IUTLO3FVW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MSTKOQDOASQEUML6IUTLO3FVW/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":"2026-05-27T20:10:30Z","links":{"resolver":"https://pith.science/pith/4MSTKOQDOASQEUML6IUTLO3FVW","bundle":"https://pith.science/pith/4MSTKOQDOASQEUML6IUTLO3FVW/bundle.json","state":"https://pith.science/pith/4MSTKOQDOASQEUML6IUTLO3FVW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MSTKOQDOASQEUML6IUTLO3FVW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4MSTKOQDOASQEUML6IUTLO3FVW","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":"7396a09729e25d11303ecb9e36b2e945400a4591f725815f21f1170a087eb03b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-20T19:05:29Z","title_canon_sha256":"8b5bb9c3e99732bde2465453b9c075c32cdfaa7a881504ab98cf34c3c5353723"},"schema_version":"1.0","source":{"id":"1311.5175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5175","created_at":"2026-05-18T03:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5175v1","created_at":"2026-05-18T03:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5175","created_at":"2026-05-18T03:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"4MSTKOQDOASQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4MSTKOQDOASQEUML","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4MSTKOQD","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:754b7e43602c48bdfb6e392766d45cee0bd4f98a13ca13e368b3d33dd2446af8","target":"graph","created_at":"2026-05-18T03:06:35Z","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 present the theory of Cauchy-Fantappi\\'e integral operators, with emphasis on the situation when the domain of integration, $D$, has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel is a holomorphic function of the parameter $z\\in D$. The goal is to prove $L^p$ estimates for these operators and, as a consequence, to obtain $L^p$ estimates for the canonical Cauchy-Szeg\\\"o and Bergman projection operators (which are not of Cauchy-Fantappi\\'e type).","authors_text":"Elias M. Stein, Loredana Lanzani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-20T19:05:29Z","title":"Cauchy-type integrals in several complex variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5175","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":"sha256:8a767e19a8d0301259c96f61b468cd303fefc69b6fb0bf76b5a89f1a29fee6a6","target":"record","created_at":"2026-05-18T03:06:35Z","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":"7396a09729e25d11303ecb9e36b2e945400a4591f725815f21f1170a087eb03b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-20T19:05:29Z","title_canon_sha256":"8b5bb9c3e99732bde2465453b9c075c32cdfaa7a881504ab98cf34c3c5353723"},"schema_version":"1.0","source":{"id":"1311.5175","kind":"arxiv","version":1}},"canonical_sha256":"e325353a03702502518bf22935bb65adb6a8a12badc8530820f569f3711f8f62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e325353a03702502518bf22935bb65adb6a8a12badc8530820f569f3711f8f62","first_computed_at":"2026-05-18T03:06:35.039937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:35.039937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BemHMV7b1uOgE4iA7tKohKvMR6kWtYUdBS6xZZuk0boPKuIlfXzwxuESihNEQrqTEHd+QTW6bkTfbbPJzhPGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:35.040638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a767e19a8d0301259c96f61b468cd303fefc69b6fb0bf76b5a89f1a29fee6a6","sha256:754b7e43602c48bdfb6e392766d45cee0bd4f98a13ca13e368b3d33dd2446af8"],"state_sha256":"62248d6e707ca71ef60568d4b70de5e3f2932a5daca065748f0b3a8de108bd92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PyNVXbmgbluvxSHO/E2gXEwzjySF6HsRJD5ielzJU8c17FgldAbyXQgK+Bmjx1uhVeV044zE0Pxh2NCNTg9kCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:10:30.170652Z","bundle_sha256":"c4bddb9d949dc506b8abf9cb857ef15d2a40c87d8034bc616cc53fb73b7611c3"}}