{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AHQIMNNS2UXRCQX7GDSE2PHYZK","short_pith_number":"pith:AHQIMNNS","canonical_record":{"source":{"id":"1309.7123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-27T06:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"6bcddf632e762e17c3b4989fa548017a8b37a99592fc1a200ce74f3b86681eb4","abstract_canon_sha256":"0680961c662b612f39c74bbe7823adcea3f10821b08c91d4064fac1fad0dcfae"},"schema_version":"1.0"},"canonical_sha256":"01e08635b2d52f1142ff30e44d3cf8cabc2e63093ad51a9ef03b39dc8fab0991","source":{"kind":"arxiv","id":"1309.7123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7123","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7123v1","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7123","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"AHQIMNNS2UXR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AHQIMNNS2UXRCQX7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AHQIMNNS","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AHQIMNNS2UXRCQX7GDSE2PHYZK","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-27T06:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"6bcddf632e762e17c3b4989fa548017a8b37a99592fc1a200ce74f3b86681eb4","abstract_canon_sha256":"0680961c662b612f39c74bbe7823adcea3f10821b08c91d4064fac1fad0dcfae"},"schema_version":"1.0"},"canonical_sha256":"01e08635b2d52f1142ff30e44d3cf8cabc2e63093ad51a9ef03b39dc8fab0991","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:39.462631Z","signature_b64":"1LfsDDkkdU4jxfLEQlduhtN0uznwowuYFv1K9dU0pScOTNsw0tOGSC8BlQPfaesq29y3uyEL7I8wqBTr4IyAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e08635b2d52f1142ff30e44d3cf8cabc2e63093ad51a9ef03b39dc8fab0991","last_reissued_at":"2026-05-18T02:54:39.462002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:39.462002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7123","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xUrwC2x4xzRBBda7w+UZC0YZvJVv/8lhxWLdu7kNWVc6lXletfIom4n1K6f30YMa76Ul9RXPJR+7nnU0s3v0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:02:50.868248Z"},"content_sha256":"3a64221c34e52577a5d98676516dfd97c0642c7ed1ebd14c98b5f54800be4302","schema_version":"1.0","event_id":"sha256:3a64221c34e52577a5d98676516dfd97c0642c7ed1ebd14c98b5f54800be4302"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AHQIMNNS2UXRCQX7GDSE2PHYZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^p$ $(p\\geq 1)$ solutions of multidimensional BSDEs with monotone generators in general time intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lishun Xiao, Na Xu, ShengJun Fan","submitted_at":"2013-09-27T06:29:28Z","abstract_excerpt":"In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(p\\geq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of convolution and weak convergence when the generator is monotonic in $y$ and Lipschitz continuous in $z$ both non-uniformly with respect to $t$. Then we obtain the existence and uniqueness for $L^1$ solutions with an additional assumption that the generator has a sublinear growth in $z$ non-uniformly with respect to $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7123","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YeRRfDFkCsW45waZyQqQWsmRCvxJZ8K2xbSn4heDbTP+uE674NbX0IvCsyoYSADAkUwoKDCKmjMaRGCZmhntDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:02:50.868944Z"},"content_sha256":"0cd2a912f32e4581c5b16f6798b28374028858b4a92a3de1233460de397064f9","schema_version":"1.0","event_id":"sha256:0cd2a912f32e4581c5b16f6798b28374028858b4a92a3de1233460de397064f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK/bundle.json","state_url":"https://pith.science/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK/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":"2026-05-26T18:02:50Z","links":{"resolver":"https://pith.science/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK","bundle":"https://pith.science/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK/bundle.json","state":"https://pith.science/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHQIMNNS2UXRCQX7GDSE2PHYZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AHQIMNNS2UXRCQX7GDSE2PHYZK","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":"0680961c662b612f39c74bbe7823adcea3f10821b08c91d4064fac1fad0dcfae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-27T06:29:28Z","title_canon_sha256":"6bcddf632e762e17c3b4989fa548017a8b37a99592fc1a200ce74f3b86681eb4"},"schema_version":"1.0","source":{"id":"1309.7123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7123","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7123v1","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7123","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"AHQIMNNS2UXR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AHQIMNNS2UXRCQX7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AHQIMNNS","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:0cd2a912f32e4581c5b16f6798b28374028858b4a92a3de1233460de397064f9","target":"graph","created_at":"2026-05-18T02:54:39Z","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 are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(p\\geq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of convolution and weak convergence when the generator is monotonic in $y$ and Lipschitz continuous in $z$ both non-uniformly with respect to $t$. Then we obtain the existence and uniqueness for $L^1$ solutions with an additional assumption that the generator has a sublinear growth in $z$ non-uniformly with respect to $t$.","authors_text":"Lishun Xiao, Na Xu, ShengJun Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-27T06:29:28Z","title":"$L^p$ $(p\\geq 1)$ solutions of multidimensional BSDEs with monotone generators in general time intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7123","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":"sha256:3a64221c34e52577a5d98676516dfd97c0642c7ed1ebd14c98b5f54800be4302","target":"record","created_at":"2026-05-18T02:54:39Z","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":"0680961c662b612f39c74bbe7823adcea3f10821b08c91d4064fac1fad0dcfae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-27T06:29:28Z","title_canon_sha256":"6bcddf632e762e17c3b4989fa548017a8b37a99592fc1a200ce74f3b86681eb4"},"schema_version":"1.0","source":{"id":"1309.7123","kind":"arxiv","version":1}},"canonical_sha256":"01e08635b2d52f1142ff30e44d3cf8cabc2e63093ad51a9ef03b39dc8fab0991","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e08635b2d52f1142ff30e44d3cf8cabc2e63093ad51a9ef03b39dc8fab0991","first_computed_at":"2026-05-18T02:54:39.462002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:39.462002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LfsDDkkdU4jxfLEQlduhtN0uznwowuYFv1K9dU0pScOTNsw0tOGSC8BlQPfaesq29y3uyEL7I8wqBTr4IyAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:39.462631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a64221c34e52577a5d98676516dfd97c0642c7ed1ebd14c98b5f54800be4302","sha256:0cd2a912f32e4581c5b16f6798b28374028858b4a92a3de1233460de397064f9"],"state_sha256":"e8c8354a50333c839727a6f53396297960f4c371b5ec27ed2a3264aabaf15a04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTIZ9kJFhkq89Zs010xqvE0si3hoVRkeJzfenoMQzM5oogV1EpDKKqdJXwNycbo/su5Cj8uNmeoAt2HfUYiFBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:02:50.872432Z","bundle_sha256":"672e32a901cb289bfca3ebb6d4bb87a019a23ec21aeac7adf45368a23ce79c06"}}