{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:B3M4EJCPCBJ3LCGOHYUDIHAJ34","short_pith_number":"pith:B3M4EJCP","canonical_record":{"source":{"id":"math/0205107","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2002-05-10T15:18:47Z","cross_cats_sorted":[],"title_canon_sha256":"9c30cce667cde5392d1bf3c269522a6272aa367ab77ae2641fb452d4c6b768e2","abstract_canon_sha256":"49749f2fc6824cd146bbc3a2c9aa2bd2ee44bbba47068228846184abdffb9513"},"schema_version":"1.0"},"canonical_sha256":"0ed9c2244f1053b588ce3e28341c09df18bbf19ceb15fc977e20ef07c1ecb01b","source":{"kind":"arxiv","id":"math/0205107","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205107","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205107v1","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205107","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"B3M4EJCPCBJ3","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_16","alias_value":"B3M4EJCPCBJ3LCGO","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_8","alias_value":"B3M4EJCP","created_at":"2026-07-04T17:23:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:B3M4EJCPCBJ3LCGOHYUDIHAJ34","target":"record","payload":{"canonical_record":{"source":{"id":"math/0205107","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2002-05-10T15:18:47Z","cross_cats_sorted":[],"title_canon_sha256":"9c30cce667cde5392d1bf3c269522a6272aa367ab77ae2641fb452d4c6b768e2","abstract_canon_sha256":"49749f2fc6824cd146bbc3a2c9aa2bd2ee44bbba47068228846184abdffb9513"},"schema_version":"1.0"},"canonical_sha256":"0ed9c2244f1053b588ce3e28341c09df18bbf19ceb15fc977e20ef07c1ecb01b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:23:15.061360Z","signature_b64":"1G8ZL2bz9nHh1W4xusALfT8R/+16mukrKP//00KYnmjhCPZZ35m4kYT/Zonh1AkVLmxW6r0RpHpQYXPO1kx+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ed9c2244f1053b588ce3e28341c09df18bbf19ceb15fc977e20ef07c1ecb01b","last_reissued_at":"2026-07-04T17:23:15.060976Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:23:15.060976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0205107","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":"2026-07-04T17:23:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQpWWmLQ3IP1EAm34/V+Wt10CvxV8joO0+HviYYKdl+uqo23qbSEHsoRCU90Ql+N0tLI6Lxj6qkXXXxlkWnbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:03:15.142449Z"},"content_sha256":"f437a2fa5b7b85db9a3644c66adfb8ffb00231e7c54d23b66121e8304d8f0eb4","schema_version":"1.0","event_id":"sha256:f437a2fa5b7b85db9a3644c66adfb8ffb00231e7c54d23b66121e8304d8f0eb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:B3M4EJCPCBJ3LCGOHYUDIHAJ34","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for singular fractional integrals and related Fourier integral operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Stephen Wainger","submitted_at":"2002-05-10T15:18:47Z","abstract_excerpt":"We prove sharp L^p-L^q endpoint bounds for singular fractional integral operators and related Fourier integral operators, under the nonvanishing rotational curvature assumption."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205107","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0205107/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:23:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrMFF1Oe0rf+S/TWDWaVkQKBFkMsSztEPtuhitJIGIay5xYYAVqDsEuID1BLmP+TBu3jHAAdQLwoyYLWnR5cBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:03:15.148264Z"},"content_sha256":"208df025188c59a45b2ddb71b73ea493f593268a0adde4adf272406efe050f04","schema_version":"1.0","event_id":"sha256:208df025188c59a45b2ddb71b73ea493f593268a0adde4adf272406efe050f04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34/bundle.json","state_url":"https://pith.science/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34/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":"2026-08-05T17:03:15Z","links":{"resolver":"https://pith.science/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34","bundle":"https://pith.science/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34/bundle.json","state":"https://pith.science/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3M4EJCPCBJ3LCGOHYUDIHAJ34/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:B3M4EJCPCBJ3LCGOHYUDIHAJ34","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":"49749f2fc6824cd146bbc3a2c9aa2bd2ee44bbba47068228846184abdffb9513","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2002-05-10T15:18:47Z","title_canon_sha256":"9c30cce667cde5392d1bf3c269522a6272aa367ab77ae2641fb452d4c6b768e2"},"schema_version":"1.0","source":{"id":"math/0205107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205107","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205107v1","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205107","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"B3M4EJCPCBJ3","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_16","alias_value":"B3M4EJCPCBJ3LCGO","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_8","alias_value":"B3M4EJCP","created_at":"2026-07-04T17:23:15Z"}],"graph_snapshots":[{"event_id":"sha256:208df025188c59a45b2ddb71b73ea493f593268a0adde4adf272406efe050f04","target":"graph","created_at":"2026-07-04T17:23:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0205107/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove sharp L^p-L^q endpoint bounds for singular fractional integral operators and related Fourier integral operators, under the nonvanishing rotational curvature assumption.","authors_text":"Andreas Seeger, Stephen Wainger","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2002-05-10T15:18:47Z","title":"Bounds for singular fractional integrals and related Fourier integral operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205107","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:f437a2fa5b7b85db9a3644c66adfb8ffb00231e7c54d23b66121e8304d8f0eb4","target":"record","created_at":"2026-07-04T17:23:15Z","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":"49749f2fc6824cd146bbc3a2c9aa2bd2ee44bbba47068228846184abdffb9513","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2002-05-10T15:18:47Z","title_canon_sha256":"9c30cce667cde5392d1bf3c269522a6272aa367ab77ae2641fb452d4c6b768e2"},"schema_version":"1.0","source":{"id":"math/0205107","kind":"arxiv","version":1}},"canonical_sha256":"0ed9c2244f1053b588ce3e28341c09df18bbf19ceb15fc977e20ef07c1ecb01b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ed9c2244f1053b588ce3e28341c09df18bbf19ceb15fc977e20ef07c1ecb01b","first_computed_at":"2026-07-04T17:23:15.060976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:23:15.060976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1G8ZL2bz9nHh1W4xusALfT8R/+16mukrKP//00KYnmjhCPZZ35m4kYT/Zonh1AkVLmxW6r0RpHpQYXPO1kx+BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:23:15.061360Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f437a2fa5b7b85db9a3644c66adfb8ffb00231e7c54d23b66121e8304d8f0eb4","sha256:208df025188c59a45b2ddb71b73ea493f593268a0adde4adf272406efe050f04"],"state_sha256":"63d7c9d592f571c3824c631bcb8faafbffc65377449b34477254a594521ddbc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKOkUGKBvFrV0/ZDmYpjDkkeITFC3LeFpskSpid5ayLXoc2K+Cpo/VbgizPD9RJc/6l3QTKWqS/82zR6Gl8+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T17:03:15.157025Z","bundle_sha256":"a2060d9a2c7387b451d7a52db18d0257b8851deb32347a8ae9a6d30d4ad61b86"}}