{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:XU4HUPH46UJFGF6RQXPWRBZWLG","short_pith_number":"pith:XU4HUPH4","canonical_record":{"source":{"id":"2209.12349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-25T23:25:30Z","cross_cats_sorted":["cs.NA","math.NA","q-fin.CP"],"title_canon_sha256":"fb64c87687267fb11549c5a3f38fec3302d39fe8dc4e730dd953bda50fd2b001","abstract_canon_sha256":"6f48a978b484e02c7458371424c5abbf79f7202548f06d3304218188e30122f3"},"schema_version":"1.0"},"canonical_sha256":"bd387a3cfcf5125317d185df6887365993e9b00c26632cc5c89ec87aaab735a6","source":{"kind":"arxiv","id":"2209.12349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.12349","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.12349v1","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.12349","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"XU4HUPH46UJF","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"pith_short_16","alias_value":"XU4HUPH46UJFGF6R","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"pith_short_8","alias_value":"XU4HUPH4","created_at":"2026-07-05T05:00:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:XU4HUPH46UJFGF6RQXPWRBZWLG","target":"record","payload":{"canonical_record":{"source":{"id":"2209.12349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-25T23:25:30Z","cross_cats_sorted":["cs.NA","math.NA","q-fin.CP"],"title_canon_sha256":"fb64c87687267fb11549c5a3f38fec3302d39fe8dc4e730dd953bda50fd2b001","abstract_canon_sha256":"6f48a978b484e02c7458371424c5abbf79f7202548f06d3304218188e30122f3"},"schema_version":"1.0"},"canonical_sha256":"bd387a3cfcf5125317d185df6887365993e9b00c26632cc5c89ec87aaab735a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:00:51.450814Z","signature_b64":"/z5GEGHd+qwNC2ZyYqg0Rq188MSErF2eeZ3JuZ0U9d14Fu2IuaArBDpDLx0ZHanMVeO6x1hUZ1Fe3y5um/U5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd387a3cfcf5125317d185df6887365993e9b00c26632cc5c89ec87aaab735a6","last_reissued_at":"2026-07-05T05:00:51.450475Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:00:51.450475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.12349","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":"2026-07-05T05:00:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMswBW359Bd090XMKZY70U1PMgCnDLASJmXqGiCMhUXLFUX6uyBBQIcDt4VF7ZFxhU7zWN/6JGB2JcXLvaUvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:07:14.714948Z"},"content_sha256":"b2f6eaa4038220c12a58499f7dcffdf280b0129dda5affbabe214e31fc5a6708","schema_version":"1.0","event_id":"sha256:b2f6eaa4038220c12a58499f7dcffdf280b0129dda5affbabe214e31fc5a6708"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:XU4HUPH46UJFGF6RQXPWRBZWLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient evaluation of expectations of functions of a stable L\\'evy process and its extremum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","q-fin.CP"],"primary_cat":"math.PR","authors_text":"Sergei Levendorski\\u{i}, Svetlana Boyarchenko","submitted_at":"2022-09-25T23:25:30Z","abstract_excerpt":"Integral representations for expectations of functions of a stable L\\'evy process $X$ and its supremum $\\bar X$ are derived. As examples, cumulative probability distribution functions (cpdf) of $X_T, \\barX_T$, the joint cpdf of $X_T$ and $\\barX_T$, and the expectation of $(\\be X_T-\\barX_T)_+$, $\\be>1$, are considered, and efficient numerical procedures for cpdfs are developed. The most efficient numerical methods use the conformal acceleration technique and simplified trapezoid rule."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12349","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/2209.12349/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":"2026-07-05T05:00:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6F+6hUniZXKX4M5VdzkQunFRd59FcWUnH37Q4yDqp+CQri704P5LD+FCXEeC9rAp6CvXAoDzIbTILeVeK0DBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:07:14.715471Z"},"content_sha256":"51067f8d7530b1061e533ace631b9b5202deabf7cf47420ef2686f68a03aa1ae","schema_version":"1.0","event_id":"sha256:51067f8d7530b1061e533ace631b9b5202deabf7cf47420ef2686f68a03aa1ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XU4HUPH46UJFGF6RQXPWRBZWLG/bundle.json","state_url":"https://pith.science/pith/XU4HUPH46UJFGF6RQXPWRBZWLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XU4HUPH46UJFGF6RQXPWRBZWLG/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":"2026-08-19T11:07:14Z","links":{"resolver":"https://pith.science/pith/XU4HUPH46UJFGF6RQXPWRBZWLG","bundle":"https://pith.science/pith/XU4HUPH46UJFGF6RQXPWRBZWLG/bundle.json","state":"https://pith.science/pith/XU4HUPH46UJFGF6RQXPWRBZWLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XU4HUPH46UJFGF6RQXPWRBZWLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XU4HUPH46UJFGF6RQXPWRBZWLG","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":"6f48a978b484e02c7458371424c5abbf79f7202548f06d3304218188e30122f3","cross_cats_sorted":["cs.NA","math.NA","q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-25T23:25:30Z","title_canon_sha256":"fb64c87687267fb11549c5a3f38fec3302d39fe8dc4e730dd953bda50fd2b001"},"schema_version":"1.0","source":{"id":"2209.12349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.12349","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.12349v1","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.12349","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"XU4HUPH46UJF","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"pith_short_16","alias_value":"XU4HUPH46UJFGF6R","created_at":"2026-07-05T05:00:51Z"},{"alias_kind":"pith_short_8","alias_value":"XU4HUPH4","created_at":"2026-07-05T05:00:51Z"}],"graph_snapshots":[{"event_id":"sha256:51067f8d7530b1061e533ace631b9b5202deabf7cf47420ef2686f68a03aa1ae","target":"graph","created_at":"2026-07-05T05:00:51Z","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/2209.12349/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Integral representations for expectations of functions of a stable L\\'evy process $X$ and its supremum $\\bar X$ are derived. As examples, cumulative probability distribution functions (cpdf) of $X_T, \\barX_T$, the joint cpdf of $X_T$ and $\\barX_T$, and the expectation of $(\\be X_T-\\barX_T)_+$, $\\be>1$, are considered, and efficient numerical procedures for cpdfs are developed. The most efficient numerical methods use the conformal acceleration technique and simplified trapezoid rule.","authors_text":"Sergei Levendorski\\u{i}, Svetlana Boyarchenko","cross_cats":["cs.NA","math.NA","q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-25T23:25:30Z","title":"Efficient evaluation of expectations of functions of a stable L\\'evy process and its extremum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12349","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:b2f6eaa4038220c12a58499f7dcffdf280b0129dda5affbabe214e31fc5a6708","target":"record","created_at":"2026-07-05T05:00:51Z","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":"6f48a978b484e02c7458371424c5abbf79f7202548f06d3304218188e30122f3","cross_cats_sorted":["cs.NA","math.NA","q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-09-25T23:25:30Z","title_canon_sha256":"fb64c87687267fb11549c5a3f38fec3302d39fe8dc4e730dd953bda50fd2b001"},"schema_version":"1.0","source":{"id":"2209.12349","kind":"arxiv","version":1}},"canonical_sha256":"bd387a3cfcf5125317d185df6887365993e9b00c26632cc5c89ec87aaab735a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd387a3cfcf5125317d185df6887365993e9b00c26632cc5c89ec87aaab735a6","first_computed_at":"2026-07-05T05:00:51.450475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:00:51.450475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/z5GEGHd+qwNC2ZyYqg0Rq188MSErF2eeZ3JuZ0U9d14Fu2IuaArBDpDLx0ZHanMVeO6x1hUZ1Fe3y5um/U5DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:00:51.450814Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.12349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2f6eaa4038220c12a58499f7dcffdf280b0129dda5affbabe214e31fc5a6708","sha256:51067f8d7530b1061e533ace631b9b5202deabf7cf47420ef2686f68a03aa1ae"],"state_sha256":"6e0a5fa914ec3b9a599371456ab8b267aff5f377a80d85ac1341ed4e10b55e44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z43HhGSGnDK8XVVXDdyQbNj/g1GY2EwDPwwpmX7pg87WOLQDOW3rM3hIS0/pd319Uz2AuDMLsbDSjx4ebWoDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T11:07:14.721597Z","bundle_sha256":"1fed34e352daf51db19dc13568436b129b8647cd2c3cec8d9aefdb5d8755a7ae"}}