{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D2WZZSG6DTJ72JAGCGC5G24LKG","short_pith_number":"pith:D2WZZSG6","canonical_record":{"source":{"id":"1407.0876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-03T12:04:15Z","cross_cats_sorted":[],"title_canon_sha256":"f522747bde84723142735e51a44c89b35c7d8f4877f0cfe3864bc4e63909364d","abstract_canon_sha256":"8eab6022195b4962d16794b3ec26f41df1fd094c22e26a61dc7af66b2f4ade94"},"schema_version":"1.0"},"canonical_sha256":"1ead9cc8de1cd3fd24061185d36b8b519034845e7cf05504ff83b91d1880a682","source":{"kind":"arxiv","id":"1407.0876","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0876","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0876v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0876","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"D2WZZSG6DTJ7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2WZZSG6DTJ72JAG","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2WZZSG6","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D2WZZSG6DTJ72JAGCGC5G24LKG","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-03T12:04:15Z","cross_cats_sorted":[],"title_canon_sha256":"f522747bde84723142735e51a44c89b35c7d8f4877f0cfe3864bc4e63909364d","abstract_canon_sha256":"8eab6022195b4962d16794b3ec26f41df1fd094c22e26a61dc7af66b2f4ade94"},"schema_version":"1.0"},"canonical_sha256":"1ead9cc8de1cd3fd24061185d36b8b519034845e7cf05504ff83b91d1880a682","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.389487Z","signature_b64":"3exr/aJAiGXiJscq/FG32sdPH6VPcqq0Q3ihd9YEmTnVXHxwL2nDVI+x6SkaaNYz6FKgMkojhORnB3ac7ULEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ead9cc8de1cd3fd24061185d36b8b519034845e7cf05504ff83b91d1880a682","last_reissued_at":"2026-05-18T01:11:55.389149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.389149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0876","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHjXY9y5DBmtK7I/UE4WC017AsZxL4/hsEbzrDmVr8fuVolHAuzPXSepn0RsBoM1PeIfnQDhycm+N9obbWgwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:36:29.971288Z"},"content_sha256":"8d466fd300113db05484a312216e41780d7e4af7d9d42c3601fa2939e5f223f6","schema_version":"1.0","event_id":"sha256:8d466fd300113db05484a312216e41780d7e4af7d9d42c3601fa2939e5f223f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D2WZZSG6DTJ72JAGCGC5G24LKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fulvia Confortola, Jean Jacod, Marco Fuhrman","submitted_at":"2014-07-03T12:04:15Z","abstract_excerpt":"We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition holds (see Assumption (A) below), we prove existence and uniqueness results under Lipschitz conditions on the coefficients. Some counter-examples show that our assumptions are indeed needed. We use a novel approach that allows reduction to a (finite or infinite) system of deterministic differential equations, thus avoiding the use of martingale representation t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0876","kind":"arxiv","version":2},"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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"moNnOr2g82RgIaV2LxKEfFFxBmbQaah7qG5fIraYhaVQprl/ZRadS6g6xGuf5bA53PMc0h3BhWg1cVO8vrECCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:36:29.972849Z"},"content_sha256":"c807ba29dcc915425484a34924cce10bd1282c639296c0d5826dac1074958713","schema_version":"1.0","event_id":"sha256:c807ba29dcc915425484a34924cce10bd1282c639296c0d5826dac1074958713"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2WZZSG6DTJ72JAGCGC5G24LKG/bundle.json","state_url":"https://pith.science/pith/D2WZZSG6DTJ72JAGCGC5G24LKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2WZZSG6DTJ72JAGCGC5G24LKG/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":"2026-06-06T02:36:29Z","links":{"resolver":"https://pith.science/pith/D2WZZSG6DTJ72JAGCGC5G24LKG","bundle":"https://pith.science/pith/D2WZZSG6DTJ72JAGCGC5G24LKG/bundle.json","state":"https://pith.science/pith/D2WZZSG6DTJ72JAGCGC5G24LKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2WZZSG6DTJ72JAGCGC5G24LKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D2WZZSG6DTJ72JAGCGC5G24LKG","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":"8eab6022195b4962d16794b3ec26f41df1fd094c22e26a61dc7af66b2f4ade94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-03T12:04:15Z","title_canon_sha256":"f522747bde84723142735e51a44c89b35c7d8f4877f0cfe3864bc4e63909364d"},"schema_version":"1.0","source":{"id":"1407.0876","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0876","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0876v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0876","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"D2WZZSG6DTJ7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2WZZSG6DTJ72JAG","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2WZZSG6","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:c807ba29dcc915425484a34924cce10bd1282c639296c0d5826dac1074958713","target":"graph","created_at":"2026-05-18T01:11:55Z","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 address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition holds (see Assumption (A) below), we prove existence and uniqueness results under Lipschitz conditions on the coefficients. Some counter-examples show that our assumptions are indeed needed. We use a novel approach that allows reduction to a (finite or infinite) system of deterministic differential equations, thus avoiding the use of martingale representation t","authors_text":"Fulvia Confortola, Jean Jacod, Marco Fuhrman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-03T12:04:15Z","title":"Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0876","kind":"arxiv","version":2},"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":"sha256:8d466fd300113db05484a312216e41780d7e4af7d9d42c3601fa2939e5f223f6","target":"record","created_at":"2026-05-18T01:11:55Z","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":"8eab6022195b4962d16794b3ec26f41df1fd094c22e26a61dc7af66b2f4ade94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-03T12:04:15Z","title_canon_sha256":"f522747bde84723142735e51a44c89b35c7d8f4877f0cfe3864bc4e63909364d"},"schema_version":"1.0","source":{"id":"1407.0876","kind":"arxiv","version":2}},"canonical_sha256":"1ead9cc8de1cd3fd24061185d36b8b519034845e7cf05504ff83b91d1880a682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ead9cc8de1cd3fd24061185d36b8b519034845e7cf05504ff83b91d1880a682","first_computed_at":"2026-05-18T01:11:55.389149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.389149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3exr/aJAiGXiJscq/FG32sdPH6VPcqq0Q3ihd9YEmTnVXHxwL2nDVI+x6SkaaNYz6FKgMkojhORnB3ac7ULEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.389487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0876","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d466fd300113db05484a312216e41780d7e4af7d9d42c3601fa2939e5f223f6","sha256:c807ba29dcc915425484a34924cce10bd1282c639296c0d5826dac1074958713"],"state_sha256":"005007e1141ecd7222749221f972014223a24477b00df7d8a356f2a7b336adaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGYz/lel3zkkfoygCbVxE+qe0+FZcCUVPnkSuuXpc6IJrIR9Dnq4fUQ00BTlpdStJn5bM5wkGsfgwKjuvBg/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T02:36:29.987934Z","bundle_sha256":"130d7128f8b06a653ce010f0d6b865537306fb8282201b89fc2ea8fd222531bf"}}