{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZT3VSYCKHANN3ENEFOIKNPOSH6","short_pith_number":"pith:ZT3VSYCK","canonical_record":{"source":{"id":"1804.08469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-23T14:31:51Z","cross_cats_sorted":[],"title_canon_sha256":"2868a7a7c00721095eb48805bf17603dbc21463e127de1655ed6451d6068ae24","abstract_canon_sha256":"aba159b9fd617e512eb58c4af9a76af59481a077a810e5d0512c0b5fb442992e"},"schema_version":"1.0"},"canonical_sha256":"ccf759604a381add91a42b90a6bdd23f9eb474e206c7c2afe85fa1acc6771d99","source":{"kind":"arxiv","id":"1804.08469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08469","created_at":"2026-05-18T00:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08469v1","created_at":"2026-05-18T00:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08469","created_at":"2026-05-18T00:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZT3VSYCKHANN","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZT3VSYCKHANN3ENE","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZT3VSYCK","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZT3VSYCKHANN3ENEFOIKNPOSH6","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-23T14:31:51Z","cross_cats_sorted":[],"title_canon_sha256":"2868a7a7c00721095eb48805bf17603dbc21463e127de1655ed6451d6068ae24","abstract_canon_sha256":"aba159b9fd617e512eb58c4af9a76af59481a077a810e5d0512c0b5fb442992e"},"schema_version":"1.0"},"canonical_sha256":"ccf759604a381add91a42b90a6bdd23f9eb474e206c7c2afe85fa1acc6771d99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:48.252140Z","signature_b64":"eiYgdsFnfAF7vrgyEUKpKeZEJOtL6E0PhG7zDIh+maaDVnxW75b7e35wC+cUehkBNyZF27ZQIwl1JI20OpWADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccf759604a381add91a42b90a6bdd23f9eb474e206c7c2afe85fa1acc6771d99","last_reissued_at":"2026-05-18T00:17:48.251463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:48.251463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08469","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":"2026-05-18T00:17:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7gdnKCpMj5Uk6uYG8zR3EmpiHPV297Oxt/t1LrmrswPSppCjxerhrf+9mPqBkOXA1bEGbtneadZHxIZZbvHWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:32:47.492579Z"},"content_sha256":"ac85186a57f40c8ee039e470cb5852862c0b44eda38335af4569eee344088af2","schema_version":"1.0","event_id":"sha256:ac85186a57f40c8ee039e470cb5852862c0b44eda38335af4569eee344088af2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZT3VSYCKHANN3ENEFOIKNPOSH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Neumann Boundary Problem for Elliptic Partial Differential Equations with Nonlinear Divergence Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jing Zhang, Xue Yang","submitted_at":"2018-04-23T14:31:51Z","abstract_excerpt":"We prove the existence and uniqueness of weak solution of a Neumann boundary problem for an elliptic partial differential equation (PDE for short) with a singular divergence term which can only be understood in a weak sense. A probabilistic approach is applied by studying the backward stochastic differential equation (BSDE for short) corresponding to the PDE."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08469","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":"2026-05-18T00:17:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TC/XPN8g9XDbDfY9tN1FmkmmlmeuH+Unmd6ttzFbfc9LRrZ3WKWqcGPb0mEFkgpGh5+QUqdx4RyEa4PhdZJXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:32:47.492925Z"},"content_sha256":"9e062ad0e9ef6aa4527752b59cf9e8c86d636049b1745b9a81bc59d028457b63","schema_version":"1.0","event_id":"sha256:9e062ad0e9ef6aa4527752b59cf9e8c86d636049b1745b9a81bc59d028457b63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6/bundle.json","state_url":"https://pith.science/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6/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":"2026-05-28T13:32:47Z","links":{"resolver":"https://pith.science/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6","bundle":"https://pith.science/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6/bundle.json","state":"https://pith.science/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZT3VSYCKHANN3ENEFOIKNPOSH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZT3VSYCKHANN3ENEFOIKNPOSH6","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":"aba159b9fd617e512eb58c4af9a76af59481a077a810e5d0512c0b5fb442992e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-23T14:31:51Z","title_canon_sha256":"2868a7a7c00721095eb48805bf17603dbc21463e127de1655ed6451d6068ae24"},"schema_version":"1.0","source":{"id":"1804.08469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08469","created_at":"2026-05-18T00:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08469v1","created_at":"2026-05-18T00:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08469","created_at":"2026-05-18T00:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZT3VSYCKHANN","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZT3VSYCKHANN3ENE","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZT3VSYCK","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:9e062ad0e9ef6aa4527752b59cf9e8c86d636049b1745b9a81bc59d028457b63","target":"graph","created_at":"2026-05-18T00:17:48Z","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 prove the existence and uniqueness of weak solution of a Neumann boundary problem for an elliptic partial differential equation (PDE for short) with a singular divergence term which can only be understood in a weak sense. A probabilistic approach is applied by studying the backward stochastic differential equation (BSDE for short) corresponding to the PDE.","authors_text":"Jing Zhang, Xue Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-23T14:31:51Z","title":"The Neumann Boundary Problem for Elliptic Partial Differential Equations with Nonlinear Divergence Terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08469","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:ac85186a57f40c8ee039e470cb5852862c0b44eda38335af4569eee344088af2","target":"record","created_at":"2026-05-18T00:17:48Z","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":"aba159b9fd617e512eb58c4af9a76af59481a077a810e5d0512c0b5fb442992e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-23T14:31:51Z","title_canon_sha256":"2868a7a7c00721095eb48805bf17603dbc21463e127de1655ed6451d6068ae24"},"schema_version":"1.0","source":{"id":"1804.08469","kind":"arxiv","version":1}},"canonical_sha256":"ccf759604a381add91a42b90a6bdd23f9eb474e206c7c2afe85fa1acc6771d99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccf759604a381add91a42b90a6bdd23f9eb474e206c7c2afe85fa1acc6771d99","first_computed_at":"2026-05-18T00:17:48.251463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:48.251463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eiYgdsFnfAF7vrgyEUKpKeZEJOtL6E0PhG7zDIh+maaDVnxW75b7e35wC+cUehkBNyZF27ZQIwl1JI20OpWADA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:48.252140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac85186a57f40c8ee039e470cb5852862c0b44eda38335af4569eee344088af2","sha256:9e062ad0e9ef6aa4527752b59cf9e8c86d636049b1745b9a81bc59d028457b63"],"state_sha256":"144f44a091dc9836db853d0f85e5bd2aea247b08b09c92e10615b33a235e636a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xU0BWX7IzgLIfagd0qz3pwjaENUBSVL1TQPGzgfnMd24poGBGvoAbemnzmAVArIJ27Kk8SJ6Zo9GeCiBdieFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:32:47.494908Z","bundle_sha256":"6555f70d2d37059e450d06f83a4fa47ebff6062e84af6e210ef84e80cf84d9b5"}}