{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JV4Y5O5KDFRPWCF4EERI4T4UP3","short_pith_number":"pith:JV4Y5O5K","canonical_record":{"source":{"id":"1210.5364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-19T09:56:05Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"bd065903791916f364d1ce06503f55201c595d996c6f6c6bb214ae5a0bb3bca4","abstract_canon_sha256":"14024e641d0c9e5811e05b5425433b860dd7f75f71844062ce70afaaf73e2dfb"},"schema_version":"1.0"},"canonical_sha256":"4d798ebbaa1962fb08bc21228e4f947ede8099c02718a1b62f9a6a4102104c30","source":{"kind":"arxiv","id":"1210.5364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5364","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5364v2","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5364","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"JV4Y5O5KDFRP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JV4Y5O5KDFRPWCF4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JV4Y5O5K","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JV4Y5O5KDFRPWCF4EERI4T4UP3","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-19T09:56:05Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"bd065903791916f364d1ce06503f55201c595d996c6f6c6bb214ae5a0bb3bca4","abstract_canon_sha256":"14024e641d0c9e5811e05b5425433b860dd7f75f71844062ce70afaaf73e2dfb"},"schema_version":"1.0"},"canonical_sha256":"4d798ebbaa1962fb08bc21228e4f947ede8099c02718a1b62f9a6a4102104c30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:13.228855Z","signature_b64":"196qSuQaXl5k/SjyBqMbpNsCr+SSRa7vmut0c1gZInq+qZk8jWv3/kOVMTnFethusEC/q+U+D31H/oE9REKuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d798ebbaa1962fb08bc21228e4f947ede8099c02718a1b62f9a6a4102104c30","last_reissued_at":"2026-05-18T02:58:13.228085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:13.228085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5364","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":"2026-05-18T02:58:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6SWdCAmaJLsqc+vk9PjGq7BLLe8oPpCiGSEGU1pJswLlLRs5/+QHXL2Rmh9OMOmuGhNGUVgaC7L3y0nKfzP0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:09:50.387511Z"},"content_sha256":"eeaf440032e2cc6f2df607c0e310ebc06b3737569c466ce911e01db1eb005a89","schema_version":"1.0","event_id":"sha256:eeaf440032e2cc6f2df607c0e310ebc06b3737569c466ce911e01db1eb005a89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JV4Y5O5KDFRPWCF4EERI4T4UP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BSDEs with weak terminal condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Anthony R\\'eveillac (CEREMADE), Bruno Bouchard (CEREMADE, CREST), Romuald Elie (CEREMADE","submitted_at":"2012-10-19T09:56:05Z","abstract_excerpt":"We introduce a new class of Backward Stochastic Differential Equations in which the $T$-terminal value $Y_{T}$ of the solution $(Y,Z)$ is not fixed as a random variable, but only satisfies a weak constraint of the form $E[\\Psi(Y_{T})]\\ge m$, for some (possibly random) non-decreasing map $\\Psi$ and some threshold $m$. We name them \\textit{BSDEs with weak terminal condition} and obtain a representation of the minimal time $t$-values $Y_{t}$ such that $(Y,Z)$ is a supersolution of the BSDE with weak terminal condition. It provides a non-Markovian BSDE formulation of the PDE characterization obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5364","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":"2026-05-18T02:58:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbpQKN6QDoo9m8Qahhrbuyk72jbE52quph0OPlgWylNzC4dAjZ4rnGeBvDGKoxEV263jAaHQK0/kcZReVN/IBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:09:50.387857Z"},"content_sha256":"34c03f49330236970829a3b8e97a127a127142c380cf19bab55b13645ac7a32a","schema_version":"1.0","event_id":"sha256:34c03f49330236970829a3b8e97a127a127142c380cf19bab55b13645ac7a32a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3/bundle.json","state_url":"https://pith.science/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3/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":"2026-05-28T19:09:50Z","links":{"resolver":"https://pith.science/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3","bundle":"https://pith.science/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3/bundle.json","state":"https://pith.science/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JV4Y5O5KDFRPWCF4EERI4T4UP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JV4Y5O5KDFRPWCF4EERI4T4UP3","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":"14024e641d0c9e5811e05b5425433b860dd7f75f71844062ce70afaaf73e2dfb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-19T09:56:05Z","title_canon_sha256":"bd065903791916f364d1ce06503f55201c595d996c6f6c6bb214ae5a0bb3bca4"},"schema_version":"1.0","source":{"id":"1210.5364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5364","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5364v2","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5364","created_at":"2026-05-18T02:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"JV4Y5O5KDFRP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JV4Y5O5KDFRPWCF4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JV4Y5O5K","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:34c03f49330236970829a3b8e97a127a127142c380cf19bab55b13645ac7a32a","target":"graph","created_at":"2026-05-18T02:58:13Z","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 introduce a new class of Backward Stochastic Differential Equations in which the $T$-terminal value $Y_{T}$ of the solution $(Y,Z)$ is not fixed as a random variable, but only satisfies a weak constraint of the form $E[\\Psi(Y_{T})]\\ge m$, for some (possibly random) non-decreasing map $\\Psi$ and some threshold $m$. We name them \\textit{BSDEs with weak terminal condition} and obtain a representation of the minimal time $t$-values $Y_{t}$ such that $(Y,Z)$ is a supersolution of the BSDE with weak terminal condition. It provides a non-Markovian BSDE formulation of the PDE characterization obtai","authors_text":"Anthony R\\'eveillac (CEREMADE), Bruno Bouchard (CEREMADE, CREST), Romuald Elie (CEREMADE","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-19T09:56:05Z","title":"BSDEs with weak terminal condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5364","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:eeaf440032e2cc6f2df607c0e310ebc06b3737569c466ce911e01db1eb005a89","target":"record","created_at":"2026-05-18T02:58:13Z","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":"14024e641d0c9e5811e05b5425433b860dd7f75f71844062ce70afaaf73e2dfb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-19T09:56:05Z","title_canon_sha256":"bd065903791916f364d1ce06503f55201c595d996c6f6c6bb214ae5a0bb3bca4"},"schema_version":"1.0","source":{"id":"1210.5364","kind":"arxiv","version":2}},"canonical_sha256":"4d798ebbaa1962fb08bc21228e4f947ede8099c02718a1b62f9a6a4102104c30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d798ebbaa1962fb08bc21228e4f947ede8099c02718a1b62f9a6a4102104c30","first_computed_at":"2026-05-18T02:58:13.228085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:13.228085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"196qSuQaXl5k/SjyBqMbpNsCr+SSRa7vmut0c1gZInq+qZk8jWv3/kOVMTnFethusEC/q+U+D31H/oE9REKuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:13.228855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeaf440032e2cc6f2df607c0e310ebc06b3737569c466ce911e01db1eb005a89","sha256:34c03f49330236970829a3b8e97a127a127142c380cf19bab55b13645ac7a32a"],"state_sha256":"420d203e2ca5188a38aa93325dc940ed0bf6a02cb2a154f8129bfc21c43a3f21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K66+aOrF4zpZLglQKL+jvEXDLUqFwJhksJ1o3al+mIvieweYWu9mHZCHfEiya7pxxhec+2X39rGlVhau251zAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:09:50.389890Z","bundle_sha256":"146fb511401f22c1d66d09ed14d3f411b6305e380d52e9feb1b1266a56184a78"}}