{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5XRGG5YKORTXLGIU5WVEPKXLOB","short_pith_number":"pith:5XRGG5YK","canonical_record":{"source":{"id":"1009.1042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T12:45:21Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"36d659380638cc4f453291439477aa888a94fdf9cc65672945576a66f166f914","abstract_canon_sha256":"e42335d80d5f77356a081406ddaa1f0689456fed54561567b4b838b75bae3410"},"schema_version":"1.0"},"canonical_sha256":"ede263770a7467759914edaa47aaeb706797396635f5ecf20788f7968ab5296e","source":{"kind":"arxiv","id":"1009.1042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1042","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1042v1","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1042","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"5XRGG5YKORTX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5XRGG5YKORTXLGIU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5XRGG5YK","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5XRGG5YKORTXLGIU5WVEPKXLOB","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T12:45:21Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"36d659380638cc4f453291439477aa888a94fdf9cc65672945576a66f166f914","abstract_canon_sha256":"e42335d80d5f77356a081406ddaa1f0689456fed54561567b4b838b75bae3410"},"schema_version":"1.0"},"canonical_sha256":"ede263770a7467759914edaa47aaeb706797396635f5ecf20788f7968ab5296e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:24.158370Z","signature_b64":"G3MAtinuTsjHIBKi5OxOkZ5fDglpkwjA7RtoZCsK76mM5gwhYe3uPSKtPN4PSNqw/W1BYDQISS12SWeUto6UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ede263770a7467759914edaa47aaeb706797396635f5ecf20788f7968ab5296e","last_reissued_at":"2026-05-18T04:41:24.157812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:24.157812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1042","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":"2026-05-18T04:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Mnm7xa0jODYKpyNndZ1s1PClo3jT4exgdpGzPhy03M3xAF9ZoFIxMWEY136q6in7l42IUZk0RKxiU8VRtdqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:39:07.286459Z"},"content_sha256":"f4f7f0b0d54d1d37c858bf18bb96489dadf6f1a8e9e11b0d4af703068b8814a8","schema_version":"1.0","event_id":"sha256:f4f7f0b0d54d1d37c858bf18bb96489dadf6f1a8e9e11b0d4af703068b8814a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5XRGG5YKORTXLGIU5WVEPKXLOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Yuhong Xu","submitted_at":"2010-09-06T12:45:21Z","abstract_excerpt":"This paper first studies super linear G-expectation. Uniqueness and existence theorem for backward stochastic differential equations (BSDEs) under super linear expectation is established to provide probabilistic interpretation for the viscosity solution of a class of Hamilton-Jacobi-Bellman equations, including the well known Black-Scholes-Barrenblett equation, arising in the uncertainty volatility model in mathematical finance. We also show that BSDEs under super linear expectation could characterize a class of stochastic control problems. A direct connection between recursive super (sub) str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1042","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":"2026-05-18T04:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vK7hfm7nL7EXtF1377g4HTQgMKN4BHLFi3Mf2e0U92JopE5pa670nXJS23aSaDmBfWBP1NggkXLqmBAu9ckAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:39:07.286810Z"},"content_sha256":"5fbeed3e834fd71f1ed727d6b8518aa4ddeca8d10d0439902b7797fcffbfcf77","schema_version":"1.0","event_id":"sha256:5fbeed3e834fd71f1ed727d6b8518aa4ddeca8d10d0439902b7797fcffbfcf77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XRGG5YKORTXLGIU5WVEPKXLOB/bundle.json","state_url":"https://pith.science/pith/5XRGG5YKORTXLGIU5WVEPKXLOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XRGG5YKORTXLGIU5WVEPKXLOB/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":"2026-06-02T14:39:07Z","links":{"resolver":"https://pith.science/pith/5XRGG5YKORTXLGIU5WVEPKXLOB","bundle":"https://pith.science/pith/5XRGG5YKORTXLGIU5WVEPKXLOB/bundle.json","state":"https://pith.science/pith/5XRGG5YKORTXLGIU5WVEPKXLOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XRGG5YKORTXLGIU5WVEPKXLOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5XRGG5YKORTXLGIU5WVEPKXLOB","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":"e42335d80d5f77356a081406ddaa1f0689456fed54561567b4b838b75bae3410","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T12:45:21Z","title_canon_sha256":"36d659380638cc4f453291439477aa888a94fdf9cc65672945576a66f166f914"},"schema_version":"1.0","source":{"id":"1009.1042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1042","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1042v1","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1042","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"5XRGG5YKORTX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5XRGG5YKORTXLGIU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5XRGG5YK","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:5fbeed3e834fd71f1ed727d6b8518aa4ddeca8d10d0439902b7797fcffbfcf77","target":"graph","created_at":"2026-05-18T04:41:24Z","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":"This paper first studies super linear G-expectation. Uniqueness and existence theorem for backward stochastic differential equations (BSDEs) under super linear expectation is established to provide probabilistic interpretation for the viscosity solution of a class of Hamilton-Jacobi-Bellman equations, including the well known Black-Scholes-Barrenblett equation, arising in the uncertainty volatility model in mathematical finance. We also show that BSDEs under super linear expectation could characterize a class of stochastic control problems. A direct connection between recursive super (sub) str","authors_text":"Yuhong Xu","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T12:45:21Z","title":"Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1042","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:f4f7f0b0d54d1d37c858bf18bb96489dadf6f1a8e9e11b0d4af703068b8814a8","target":"record","created_at":"2026-05-18T04:41:24Z","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":"e42335d80d5f77356a081406ddaa1f0689456fed54561567b4b838b75bae3410","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T12:45:21Z","title_canon_sha256":"36d659380638cc4f453291439477aa888a94fdf9cc65672945576a66f166f914"},"schema_version":"1.0","source":{"id":"1009.1042","kind":"arxiv","version":1}},"canonical_sha256":"ede263770a7467759914edaa47aaeb706797396635f5ecf20788f7968ab5296e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ede263770a7467759914edaa47aaeb706797396635f5ecf20788f7968ab5296e","first_computed_at":"2026-05-18T04:41:24.157812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:24.157812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3MAtinuTsjHIBKi5OxOkZ5fDglpkwjA7RtoZCsK76mM5gwhYe3uPSKtPN4PSNqw/W1BYDQISS12SWeUto6UBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:24.158370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4f7f0b0d54d1d37c858bf18bb96489dadf6f1a8e9e11b0d4af703068b8814a8","sha256:5fbeed3e834fd71f1ed727d6b8518aa4ddeca8d10d0439902b7797fcffbfcf77"],"state_sha256":"c650eca434eec3b0744484f3e9bd1604c431d310a3b6e5ae7a9b6820414b1777"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vqDcbTLwM5ju6hm+Fpj8Go/FABlO/qe2Ksop8ilky2V9aP7H9foQWF8IXzhDHflYRSLCRjMpWL8QxHJczE+GCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:39:07.288721Z","bundle_sha256":"d8abb575afa2b47a8b1f95c7ebe9e4afd9b5c6203ce8100f691a7609223ffe11"}}