{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YDZKX5UAI6UMEV2VPGDKOFUQWB","short_pith_number":"pith:YDZKX5UA","canonical_record":{"source":{"id":"1612.05681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-12-16T23:54:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"46bb57fd36d35518952da5404a0843c48bd508ebc9f1a960a8c75f2f555ac824","abstract_canon_sha256":"4d6ce3ab4df60ba6a47d0870e11a3cc9ec7468c13f78546a0366661f8611f204"},"schema_version":"1.0"},"canonical_sha256":"c0f2abf68047a8c257557986a71690b0798e6f4d32dcf5cce591d45bed27c271","source":{"kind":"arxiv","id":"1612.05681","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05681","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05681v3","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05681","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"YDZKX5UAI6UM","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YDZKX5UAI6UMEV2V","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YDZKX5UA","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YDZKX5UAI6UMEV2VPGDKOFUQWB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-12-16T23:54:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"46bb57fd36d35518952da5404a0843c48bd508ebc9f1a960a8c75f2f555ac824","abstract_canon_sha256":"4d6ce3ab4df60ba6a47d0870e11a3cc9ec7468c13f78546a0366661f8611f204"},"schema_version":"1.0"},"canonical_sha256":"c0f2abf68047a8c257557986a71690b0798e6f4d32dcf5cce591d45bed27c271","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:14.334102Z","signature_b64":"xdzcuWnLYL6vgRx0K2Ekpd2/MMeTL4NR9JTri/aue8Wyda/Y36D231WpvYqX/UFAGuZFU4y2cnMoAHak5uP8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0f2abf68047a8c257557986a71690b0798e6f4d32dcf5cce591d45bed27c271","last_reissued_at":"2026-05-18T00:36:14.333494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:14.333494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05681","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+J7Y7g+FAaWrHDOgf9HzKf1W6GBW9WRQfp4PRBuPOTxTRUukansmC+MoXqLRl//Rh/0f4MtIpXPoxC870o6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:56:50.466221Z"},"content_sha256":"fffe519c35bc90b8a6c93c756599c8225b136d5125b416d68be20ab6a6d59744","schema_version":"1.0","event_id":"sha256:fffe519c35bc90b8a6c93c756599c8225b136d5125b416d68be20ab6a6d59744"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YDZKX5UAI6UMEV2VPGDKOFUQWB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BSDEs with default jump","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Agn\\`Es Sulem, Marie-Claire Quenez, Roxana Dumitrescu","submitted_at":"2016-12-16T23:54:04Z","abstract_excerpt":"We study the properties of nonlinear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale measure associated with a default jump with intensity process $(\\lambda_t)$. We give a priori estimates for these equations and prove comparison and strict comparison theorems. These results are generalized to drivers involving a singular process. The special case of a $\\lambda$-linear driver is studied, leading to a representation of the solution of the associated BSDE in terms of a conditional expectation and an adjoint exponential semi-martingale. We then appl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05681","kind":"arxiv","version":3},"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":"2026-05-18T00:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmRSt7s9Ju/oYkCYjULnykMfa2NzLU0GLSoAjs3rWnO0ybYwOD2WXSIv6X2Afwx75Sre35hrgG9AJDVRkQssDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:56:50.466892Z"},"content_sha256":"c3fee87a488c759aa2e0069a319d7263383b77959536c66d0f39fd6128690a29","schema_version":"1.0","event_id":"sha256:c3fee87a488c759aa2e0069a319d7263383b77959536c66d0f39fd6128690a29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB/bundle.json","state_url":"https://pith.science/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB/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":"2026-05-30T08:56:50Z","links":{"resolver":"https://pith.science/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB","bundle":"https://pith.science/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB/bundle.json","state":"https://pith.science/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDZKX5UAI6UMEV2VPGDKOFUQWB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YDZKX5UAI6UMEV2VPGDKOFUQWB","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":"4d6ce3ab4df60ba6a47d0870e11a3cc9ec7468c13f78546a0366661f8611f204","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-12-16T23:54:04Z","title_canon_sha256":"46bb57fd36d35518952da5404a0843c48bd508ebc9f1a960a8c75f2f555ac824"},"schema_version":"1.0","source":{"id":"1612.05681","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05681","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05681v3","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05681","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"YDZKX5UAI6UM","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YDZKX5UAI6UMEV2V","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YDZKX5UA","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:c3fee87a488c759aa2e0069a319d7263383b77959536c66d0f39fd6128690a29","target":"graph","created_at":"2026-05-18T00:36:14Z","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 study the properties of nonlinear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale measure associated with a default jump with intensity process $(\\lambda_t)$. We give a priori estimates for these equations and prove comparison and strict comparison theorems. These results are generalized to drivers involving a singular process. The special case of a $\\lambda$-linear driver is studied, leading to a representation of the solution of the associated BSDE in terms of a conditional expectation and an adjoint exponential semi-martingale. We then appl","authors_text":"Agn\\`Es Sulem, Marie-Claire Quenez, Roxana Dumitrescu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-12-16T23:54:04Z","title":"BSDEs with default jump"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05681","kind":"arxiv","version":3},"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:fffe519c35bc90b8a6c93c756599c8225b136d5125b416d68be20ab6a6d59744","target":"record","created_at":"2026-05-18T00:36:14Z","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":"4d6ce3ab4df60ba6a47d0870e11a3cc9ec7468c13f78546a0366661f8611f204","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-12-16T23:54:04Z","title_canon_sha256":"46bb57fd36d35518952da5404a0843c48bd508ebc9f1a960a8c75f2f555ac824"},"schema_version":"1.0","source":{"id":"1612.05681","kind":"arxiv","version":3}},"canonical_sha256":"c0f2abf68047a8c257557986a71690b0798e6f4d32dcf5cce591d45bed27c271","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0f2abf68047a8c257557986a71690b0798e6f4d32dcf5cce591d45bed27c271","first_computed_at":"2026-05-18T00:36:14.333494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:14.333494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xdzcuWnLYL6vgRx0K2Ekpd2/MMeTL4NR9JTri/aue8Wyda/Y36D231WpvYqX/UFAGuZFU4y2cnMoAHak5uP8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:14.334102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05681","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fffe519c35bc90b8a6c93c756599c8225b136d5125b416d68be20ab6a6d59744","sha256:c3fee87a488c759aa2e0069a319d7263383b77959536c66d0f39fd6128690a29"],"state_sha256":"d78d3bd731888314e24bf3ce8bd7b074336b7d05ba0ced88df9c9d74f904aeb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"StdVtjcMRRW9KwfFIlhZNNTm5yEsvlI1YpRlUpbRFIVvPA7ChwcV3XNO16GdjhMbz1iTftZYw362rSwZ8O9rBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:56:50.470189Z","bundle_sha256":"a447d5fd94434b7731d402c0fcd73eaf6a7fb16393c342e5f863a5aa987fe347"}}