{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4CKAVZYVWDMRELEJ7JF6VGCOQP","short_pith_number":"pith:4CKAVZYV","canonical_record":{"source":{"id":"1110.3254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-14T15:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"1b2e753eab4e8888c01ff1b53a911bc0aef2741b6b347490a5f0f2c518342996","abstract_canon_sha256":"650cbcfca43d54b3919909b2735d418f9b29735e1dfcf707ea322f25caa7fffb"},"schema_version":"1.0"},"canonical_sha256":"e0940ae715b0d9122c89fa4bea984e83f7d6f2ea100042e78658a9ed4d287cac","source":{"kind":"arxiv","id":"1110.3254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3254","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3254v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3254","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"4CKAVZYVWDMR","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4CKAVZYVWDMRELEJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4CKAVZYV","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4CKAVZYVWDMRELEJ7JF6VGCOQP","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-14T15:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"1b2e753eab4e8888c01ff1b53a911bc0aef2741b6b347490a5f0f2c518342996","abstract_canon_sha256":"650cbcfca43d54b3919909b2735d418f9b29735e1dfcf707ea322f25caa7fffb"},"schema_version":"1.0"},"canonical_sha256":"e0940ae715b0d9122c89fa4bea984e83f7d6f2ea100042e78658a9ed4d287cac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.673561Z","signature_b64":"B5ioexxGKZFum23LQ4No1zdZm1d+FaKd/o5R/iDxVq6/TVRK8kpDW4n51i0CKqvuJxG4/zfLL+Mq63zpfPo4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0940ae715b0d9122c89fa4bea984e83f7d6f2ea100042e78658a9ed4d287cac","last_reissued_at":"2026-05-18T04:10:57.673113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.673113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3254","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0x0QuxpWG14jg0Y+LKX3vjVDFkMkv/waPOe8IVLcYI2AAbY0QAZlgOu8brhFKWwCcdUgIHsVp8iyd35L5IlNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:51:29.354113Z"},"content_sha256":"fb9ecc867d3043fbb7d3f9ee389219c863c81b80ee24e5032d5929174a1ad106","schema_version":"1.0","event_id":"sha256:fb9ecc867d3043fbb7d3f9ee389219c863c81b80ee24e5032d5929174a1ad106"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4CKAVZYVWDMRELEJ7JF6VGCOQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal Supersolutions of BSDEs with Lower Semicontinuous Generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christoph Mainberger, Gregor Heyne, Michael Kupper","submitted_at":"2011-10-14T15:58:43Z","abstract_excerpt":"We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a specific normalization property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3254","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dGBZwboNmdHxSFHbfoSCJAdwgthIzm6Er3OMJ7tVWHjxO3NB/FA6S+8VTYgEsKgpOvivKgDpFQZfxBsK6FoXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:51:29.354462Z"},"content_sha256":"86842483f67d51e3005fb52b1a299332e2392c8136730628a5b717df3bf9deee","schema_version":"1.0","event_id":"sha256:86842483f67d51e3005fb52b1a299332e2392c8136730628a5b717df3bf9deee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP/bundle.json","state_url":"https://pith.science/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP/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":"2026-06-27T16:51:29Z","links":{"resolver":"https://pith.science/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP","bundle":"https://pith.science/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP/bundle.json","state":"https://pith.science/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CKAVZYVWDMRELEJ7JF6VGCOQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4CKAVZYVWDMRELEJ7JF6VGCOQP","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":"650cbcfca43d54b3919909b2735d418f9b29735e1dfcf707ea322f25caa7fffb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-14T15:58:43Z","title_canon_sha256":"1b2e753eab4e8888c01ff1b53a911bc0aef2741b6b347490a5f0f2c518342996"},"schema_version":"1.0","source":{"id":"1110.3254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3254","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3254v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3254","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"4CKAVZYVWDMR","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4CKAVZYVWDMRELEJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4CKAVZYV","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:86842483f67d51e3005fb52b1a299332e2392c8136730628a5b717df3bf9deee","target":"graph","created_at":"2026-05-18T04:10:57Z","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 study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a specific normalization property.","authors_text":"Christoph Mainberger, Gregor Heyne, Michael Kupper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-14T15:58:43Z","title":"Minimal Supersolutions of BSDEs with Lower Semicontinuous Generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3254","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:fb9ecc867d3043fbb7d3f9ee389219c863c81b80ee24e5032d5929174a1ad106","target":"record","created_at":"2026-05-18T04:10:57Z","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":"650cbcfca43d54b3919909b2735d418f9b29735e1dfcf707ea322f25caa7fffb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-14T15:58:43Z","title_canon_sha256":"1b2e753eab4e8888c01ff1b53a911bc0aef2741b6b347490a5f0f2c518342996"},"schema_version":"1.0","source":{"id":"1110.3254","kind":"arxiv","version":1}},"canonical_sha256":"e0940ae715b0d9122c89fa4bea984e83f7d6f2ea100042e78658a9ed4d287cac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0940ae715b0d9122c89fa4bea984e83f7d6f2ea100042e78658a9ed4d287cac","first_computed_at":"2026-05-18T04:10:57.673113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:57.673113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B5ioexxGKZFum23LQ4No1zdZm1d+FaKd/o5R/iDxVq6/TVRK8kpDW4n51i0CKqvuJxG4/zfLL+Mq63zpfPo4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:57.673561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb9ecc867d3043fbb7d3f9ee389219c863c81b80ee24e5032d5929174a1ad106","sha256:86842483f67d51e3005fb52b1a299332e2392c8136730628a5b717df3bf9deee"],"state_sha256":"9ebadcdfd6aed5bf11eca1c589531784d7180d5517220c324fddd677ec630df1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Yz2HyxKGwOcK946o5xcBopwBsaC+ZzhIsLh2k7PADDEKl/mM2N99Tbk0WMvo25lrYiGmj+YXUeFx7eHpCBtDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:51:29.356299Z","bundle_sha256":"3f973b520cc7548a9ce9c31648637748fb99882e2ed0ac304cf92983982ae81f"}}