{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PEZ5YSITMZPAPD4VFLIYGLTE4P","short_pith_number":"pith:PEZ5YSIT","canonical_record":{"source":{"id":"1704.05212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T06:32:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c0155e566767e9c52f60d3c361e97f80ec6933af9756cfe65b1f941b9766190","abstract_canon_sha256":"6715ca35b2a45f2d1e4bf88c9be1cd8a9787d74da11c952a83d57b48897862e3"},"schema_version":"1.0"},"canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","source":{"kind":"arxiv","id":"1704.05212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05212","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05212v1","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05212","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"PEZ5YSITMZPA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PEZ5YSITMZPAPD4V","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PEZ5YSIT","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PEZ5YSITMZPAPD4VFLIYGLTE4P","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T06:32:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c0155e566767e9c52f60d3c361e97f80ec6933af9756cfe65b1f941b9766190","abstract_canon_sha256":"6715ca35b2a45f2d1e4bf88c9be1cd8a9787d74da11c952a83d57b48897862e3"},"schema_version":"1.0"},"canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:11.513508Z","signature_b64":"gGRmWzfVBpjTVD89LFT08h2Nkl1/5vI73PKY07He+a1LhbXqzF3W2lTZ/hFk0+CAaDyUOYL+gvVVWlSBgBK7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","last_reissued_at":"2026-05-18T00:46:11.513062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:11.513062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05212","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":"2026-05-18T00:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7z231LyIwqBSq/Q7Dfc7YJNf9/GkXE3LXGipDKc1GsZbAU7leraT2CNFlT+igaQYNlZ9vHpxKe7IbqbZDG8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:58:57.154091Z"},"content_sha256":"c57477fb45c69ebe822bbae588e0e488cead06b69530a3cb34e6d0e4cca4f7d7","schema_version":"1.0","event_id":"sha256:c57477fb45c69ebe822bbae588e0e488cead06b69530a3cb34e6d0e4cca4f7d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PEZ5YSITMZPAPD4VFLIYGLTE4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shanjian Tang (School of Mathematical Sciences), Ying Hu (IRMAR)","submitted_at":"2017-04-18T06:32:24Z","abstract_excerpt":"In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some $\\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\\log L$ integrability.  We show by a counterexample that $L\\log L$ integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05212","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":""},"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":"2026-05-18T00:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkFtPrseZERPGazVmlANfbWK7TcYjw6DmIYyLV7fWc2JQCV5/efKeeopTmjk/bKmaAG4pdFeSW+jP5UI4vPFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:58:57.154439Z"},"content_sha256":"555f0b4baea90dfa6af59328f396c425820338a3189a692596c61b0ab5418a78","schema_version":"1.0","event_id":"sha256:555f0b4baea90dfa6af59328f396c425820338a3189a692596c61b0ab5418a78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/bundle.json","state_url":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/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":"2026-07-04T09:58:57Z","links":{"resolver":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P","bundle":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/bundle.json","state":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PEZ5YSITMZPAPD4VFLIYGLTE4P","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":"6715ca35b2a45f2d1e4bf88c9be1cd8a9787d74da11c952a83d57b48897862e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T06:32:24Z","title_canon_sha256":"1c0155e566767e9c52f60d3c361e97f80ec6933af9756cfe65b1f941b9766190"},"schema_version":"1.0","source":{"id":"1704.05212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05212","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05212v1","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05212","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"PEZ5YSITMZPA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PEZ5YSITMZPAPD4V","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PEZ5YSIT","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:555f0b4baea90dfa6af59328f396c425820338a3189a692596c61b0ab5418a78","target":"graph","created_at":"2026-05-18T00:46:11Z","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":"In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some $\\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\\log L$ integrability.  We show by a counterexample that $L\\log L$ integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator.","authors_text":"Shanjian Tang (School of Mathematical Sciences), Ying Hu (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T06:32:24Z","title":"Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05212","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:c57477fb45c69ebe822bbae588e0e488cead06b69530a3cb34e6d0e4cca4f7d7","target":"record","created_at":"2026-05-18T00:46:11Z","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":"6715ca35b2a45f2d1e4bf88c9be1cd8a9787d74da11c952a83d57b48897862e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T06:32:24Z","title_canon_sha256":"1c0155e566767e9c52f60d3c361e97f80ec6933af9756cfe65b1f941b9766190"},"schema_version":"1.0","source":{"id":"1704.05212","kind":"arxiv","version":1}},"canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","first_computed_at":"2026-05-18T00:46:11.513062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:11.513062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gGRmWzfVBpjTVD89LFT08h2Nkl1/5vI73PKY07He+a1LhbXqzF3W2lTZ/hFk0+CAaDyUOYL+gvVVWlSBgBK7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:11.513508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c57477fb45c69ebe822bbae588e0e488cead06b69530a3cb34e6d0e4cca4f7d7","sha256:555f0b4baea90dfa6af59328f396c425820338a3189a692596c61b0ab5418a78"],"state_sha256":"849c8b80d384da146f1584ca63eb82a1ba09b75477b84715e6e224acc3b3ebe8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"us6yHGhrYTlKGLxFwaJeYpufoLrCr6uEUMJI/m+IgWTWYRPMSURez0WO88qfbpbCrUhqpihZTXv+QkdASuZBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T09:58:57.156289Z","bundle_sha256":"19c7449d40a3da0f3ea28e5b14ed1c3f9a714a50784ea610e3562ca99561aac0"}}