{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:744TABU7TUEINM32XV2E5TIBFC","short_pith_number":"pith:744TABU7","canonical_record":{"source":{"id":"1804.10970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-29T17:41:53Z","cross_cats_sorted":[],"title_canon_sha256":"38d331ab178ff8d9ea54436539fdeea20ab319787aba32ac8984bc201defcb70","abstract_canon_sha256":"813cfdc39e705545b4905b9ed44ea8ad324c69ba4bc3e975a95f4892e47aef0f"},"schema_version":"1.0"},"canonical_sha256":"ff3930069f9d0886b37abd744ecd0128b1caa160202567cdd307c2900855dcb0","source":{"kind":"arxiv","id":"1804.10970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10970","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10970v1","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10970","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"744TABU7TUEI","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"744TABU7TUEINM32","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"744TABU7","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:744TABU7TUEINM32XV2E5TIBFC","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-29T17:41:53Z","cross_cats_sorted":[],"title_canon_sha256":"38d331ab178ff8d9ea54436539fdeea20ab319787aba32ac8984bc201defcb70","abstract_canon_sha256":"813cfdc39e705545b4905b9ed44ea8ad324c69ba4bc3e975a95f4892e47aef0f"},"schema_version":"1.0"},"canonical_sha256":"ff3930069f9d0886b37abd744ecd0128b1caa160202567cdd307c2900855dcb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:15.029167Z","signature_b64":"AnXgyroZeln4DKFbL6222UmWqFkycQdY1IkmglBxRh02SPL7tS5KtuSf/RRk//YDIz6McdXgDgtE4q/QfQojAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff3930069f9d0886b37abd744ecd0128b1caa160202567cdd307c2900855dcb0","last_reissued_at":"2026-05-18T00:17:15.028301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:15.028301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10970","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":"2026-05-18T00:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ts8KPxgA5DOnxlKcD/Dyycpzkz4cqX+cBn0QH/3YF1g65+WRtOkJPjnedyEXg+KtecSy498lbp7hmC5+/Hh2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:34:34.007899Z"},"content_sha256":"0e301f75af787a4c6fa9a9981e431b575bf525a4fc9e5b2b1a3bb10b621943db","schema_version":"1.0","event_id":"sha256:0e301f75af787a4c6fa9a9981e431b575bf525a4fc9e5b2b1a3bb10b621943db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:744TABU7TUEINM32XV2E5TIBFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The method of decoupling fields generalized to higher spatial derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Fromm","submitted_at":"2018-04-29T17:41:53Z","abstract_excerpt":"This work studies the spatial derivatives of decoupling fields to strongly coupled forward-backward stochastic differential equations in a Brownian setting. We formally deduce the backward dynamics of the first and higher spatial derivatives. In addition, we study necessary conditions under which singularities in either one of them can occur while moving backwards in time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10970","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":"2026-05-18T00:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tle2jsLHohJMXZitghdfkrfOYeZ4QfmNbGl/omKieq4j3PZICuQtc37irvPtMRJDV764ozXqQCCUzn15SiACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:34:34.008558Z"},"content_sha256":"9bc0fec4c4bdacf900ba12fd2eebe50d4670878fec193c011d1bb53c05bbea77","schema_version":"1.0","event_id":"sha256:9bc0fec4c4bdacf900ba12fd2eebe50d4670878fec193c011d1bb53c05bbea77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/744TABU7TUEINM32XV2E5TIBFC/bundle.json","state_url":"https://pith.science/pith/744TABU7TUEINM32XV2E5TIBFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/744TABU7TUEINM32XV2E5TIBFC/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":"2026-06-01T08:34:34Z","links":{"resolver":"https://pith.science/pith/744TABU7TUEINM32XV2E5TIBFC","bundle":"https://pith.science/pith/744TABU7TUEINM32XV2E5TIBFC/bundle.json","state":"https://pith.science/pith/744TABU7TUEINM32XV2E5TIBFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/744TABU7TUEINM32XV2E5TIBFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:744TABU7TUEINM32XV2E5TIBFC","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":"813cfdc39e705545b4905b9ed44ea8ad324c69ba4bc3e975a95f4892e47aef0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-29T17:41:53Z","title_canon_sha256":"38d331ab178ff8d9ea54436539fdeea20ab319787aba32ac8984bc201defcb70"},"schema_version":"1.0","source":{"id":"1804.10970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10970","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10970v1","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10970","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"744TABU7TUEI","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"744TABU7TUEINM32","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"744TABU7","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:9bc0fec4c4bdacf900ba12fd2eebe50d4670878fec193c011d1bb53c05bbea77","target":"graph","created_at":"2026-05-18T00:17:15Z","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 work studies the spatial derivatives of decoupling fields to strongly coupled forward-backward stochastic differential equations in a Brownian setting. We formally deduce the backward dynamics of the first and higher spatial derivatives. In addition, we study necessary conditions under which singularities in either one of them can occur while moving backwards in time.","authors_text":"Alexander Fromm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-29T17:41:53Z","title":"The method of decoupling fields generalized to higher spatial derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10970","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":"sha256:0e301f75af787a4c6fa9a9981e431b575bf525a4fc9e5b2b1a3bb10b621943db","target":"record","created_at":"2026-05-18T00:17:15Z","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":"813cfdc39e705545b4905b9ed44ea8ad324c69ba4bc3e975a95f4892e47aef0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-29T17:41:53Z","title_canon_sha256":"38d331ab178ff8d9ea54436539fdeea20ab319787aba32ac8984bc201defcb70"},"schema_version":"1.0","source":{"id":"1804.10970","kind":"arxiv","version":1}},"canonical_sha256":"ff3930069f9d0886b37abd744ecd0128b1caa160202567cdd307c2900855dcb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff3930069f9d0886b37abd744ecd0128b1caa160202567cdd307c2900855dcb0","first_computed_at":"2026-05-18T00:17:15.028301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:15.028301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AnXgyroZeln4DKFbL6222UmWqFkycQdY1IkmglBxRh02SPL7tS5KtuSf/RRk//YDIz6McdXgDgtE4q/QfQojAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:15.029167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e301f75af787a4c6fa9a9981e431b575bf525a4fc9e5b2b1a3bb10b621943db","sha256:9bc0fec4c4bdacf900ba12fd2eebe50d4670878fec193c011d1bb53c05bbea77"],"state_sha256":"d4c3c1209523f8e740648fbd8d2b5c66be67f4cb8247bcb45e92b54e6d66ee12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C165stkE1tcCmp1SSCVXSi3TPQjooQPvn0Z9JcF789hjyx9+RVlFDoXNvvKGL3dZoUcRHlKBs3yH+Zfh09NrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:34:34.011629Z","bundle_sha256":"da9251e8fa49a41230df042d54d42632f1e5a3bfaf9fff32a2a6d03a6b8fccab"}}