{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3MBH5TRTUS4E27BS7O6NMYTYRN","short_pith_number":"pith:3MBH5TRT","canonical_record":{"source":{"id":"1309.3829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-16T04:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"590296d1cb1b281286bb9243f4aa17d8732a6376525a918c05937d6e5aa9a3af","abstract_canon_sha256":"914f76821d75da6909913847c0695db1bac2282d3399c37a4a4255bb70981311"},"schema_version":"1.0"},"canonical_sha256":"db027ece33a4b84d7c32fbbcd662788b4ecc30c30fadad3deefce762db379392","source":{"kind":"arxiv","id":"1309.3829","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3829","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3829v1","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3829","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"3MBH5TRTUS4E","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3MBH5TRTUS4E27BS","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3MBH5TRT","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3MBH5TRTUS4E27BS7O6NMYTYRN","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-16T04:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"590296d1cb1b281286bb9243f4aa17d8732a6376525a918c05937d6e5aa9a3af","abstract_canon_sha256":"914f76821d75da6909913847c0695db1bac2282d3399c37a4a4255bb70981311"},"schema_version":"1.0"},"canonical_sha256":"db027ece33a4b84d7c32fbbcd662788b4ecc30c30fadad3deefce762db379392","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:20.444932Z","signature_b64":"Vi+7XeIZZq/rVXzhcdpYSFon+dhY+HriLulHO9T6X9GRzmL8U9cOSjK1R/B8cwJCU/SWGah7OyWKVUYj6h7tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db027ece33a4b84d7c32fbbcd662788b4ecc30c30fadad3deefce762db379392","last_reissued_at":"2026-05-18T03:13:20.444445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:20.444445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3829","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":"2026-05-18T03:13:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9XbvNo9mkLpNb7A1DFDg9jWnYMz8wOwbltglFqIPpr6JjkpLZYWXj4b+EvEMLPsXUJo+8oD+ALvkLjxK0x+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:41:23.133675Z"},"content_sha256":"2c26661d8f7d5381e8d83915a52a5c3405e28f2ee862aef6036741b827157b70","schema_version":"1.0","event_id":"sha256:2c26661d8f7d5381e8d83915a52a5c3405e28f2ee862aef6036741b827157b70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3MBH5TRTUS4E27BS7O6NMYTYRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended Conditional G-Expectations and Related Stopping Times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mingshang Hu, Shige Peng","submitted_at":"2013-09-16T04:42:04Z","abstract_excerpt":"In this paper we extend the definition of time conditional G-expectations $\\mathbb{\\hat{E}}_{t}[\\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time conditional expectations for each random variable $X$ which is the downward limit (resp. upward limit) of a monotone sequence $\\{X_{i}\\}$ in $L_{G}^{1}(\\Omega)$. To accomplish this procedure, some careful analysis is needed. Moreover, we give a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3829","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":"2026-05-18T03:13:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jztm8sRMI1gW8a4RoFqnwaXcMzmSGJ59WcuD4iE/KmQj29MD99nVpxTW9r4Wxa9Il08sYPGLfzt5yyU3FyuaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:41:23.134026Z"},"content_sha256":"c4cb5800a2ab0aa9154798c0fb94e5a9d6aebbca2e3001cb9d481148fdc445c1","schema_version":"1.0","event_id":"sha256:c4cb5800a2ab0aa9154798c0fb94e5a9d6aebbca2e3001cb9d481148fdc445c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MBH5TRTUS4E27BS7O6NMYTYRN/bundle.json","state_url":"https://pith.science/pith/3MBH5TRTUS4E27BS7O6NMYTYRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MBH5TRTUS4E27BS7O6NMYTYRN/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":"2026-06-11T09:41:23Z","links":{"resolver":"https://pith.science/pith/3MBH5TRTUS4E27BS7O6NMYTYRN","bundle":"https://pith.science/pith/3MBH5TRTUS4E27BS7O6NMYTYRN/bundle.json","state":"https://pith.science/pith/3MBH5TRTUS4E27BS7O6NMYTYRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MBH5TRTUS4E27BS7O6NMYTYRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3MBH5TRTUS4E27BS7O6NMYTYRN","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":"914f76821d75da6909913847c0695db1bac2282d3399c37a4a4255bb70981311","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-16T04:42:04Z","title_canon_sha256":"590296d1cb1b281286bb9243f4aa17d8732a6376525a918c05937d6e5aa9a3af"},"schema_version":"1.0","source":{"id":"1309.3829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3829","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3829v1","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3829","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"3MBH5TRTUS4E","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3MBH5TRTUS4E27BS","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3MBH5TRT","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:c4cb5800a2ab0aa9154798c0fb94e5a9d6aebbca2e3001cb9d481148fdc445c1","target":"graph","created_at":"2026-05-18T03:13:20Z","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 extend the definition of time conditional G-expectations $\\mathbb{\\hat{E}}_{t}[\\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time conditional expectations for each random variable $X$ which is the downward limit (resp. upward limit) of a monotone sequence $\\{X_{i}\\}$ in $L_{G}^{1}(\\Omega)$. To accomplish this procedure, some careful analysis is needed. Moreover, we give a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interes","authors_text":"Mingshang Hu, Shige Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-16T04:42:04Z","title":"Extended Conditional G-Expectations and Related Stopping Times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3829","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":"sha256:2c26661d8f7d5381e8d83915a52a5c3405e28f2ee862aef6036741b827157b70","target":"record","created_at":"2026-05-18T03:13:20Z","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":"914f76821d75da6909913847c0695db1bac2282d3399c37a4a4255bb70981311","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-16T04:42:04Z","title_canon_sha256":"590296d1cb1b281286bb9243f4aa17d8732a6376525a918c05937d6e5aa9a3af"},"schema_version":"1.0","source":{"id":"1309.3829","kind":"arxiv","version":1}},"canonical_sha256":"db027ece33a4b84d7c32fbbcd662788b4ecc30c30fadad3deefce762db379392","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db027ece33a4b84d7c32fbbcd662788b4ecc30c30fadad3deefce762db379392","first_computed_at":"2026-05-18T03:13:20.444445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:20.444445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vi+7XeIZZq/rVXzhcdpYSFon+dhY+HriLulHO9T6X9GRzmL8U9cOSjK1R/B8cwJCU/SWGah7OyWKVUYj6h7tAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:20.444932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c26661d8f7d5381e8d83915a52a5c3405e28f2ee862aef6036741b827157b70","sha256:c4cb5800a2ab0aa9154798c0fb94e5a9d6aebbca2e3001cb9d481148fdc445c1"],"state_sha256":"329f1880afee38d78a1b1b70f0ddabb7dd112cd9b31f6748ab9941e6324ccc49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A52ztiqUgdlZKB8znJxJv4AjixYVYHEkC23WiHVqmD4I+5+JDpwwSwna05HtRzWJHK/J15uIgRa+Bh0glfNDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:41:23.135941Z","bundle_sha256":"430fc87b76e19a6a71daeb7ae4dcbd2ce03579602dac9924d2ed0a8f4625cd98"}}