{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:25NOLI4P47ABJFYF47NIEZPIKQ","short_pith_number":"pith:25NOLI4P","canonical_record":{"source":{"id":"1503.05433","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-18T14:43:30Z","cross_cats_sorted":[],"title_canon_sha256":"bd20008423390d214d392137f3b3e32b2d2783ebbb277e6da460599f66fd100c","abstract_canon_sha256":"5ce9f40838e40617922003b0a0eee9958ca5233248b0dbd8ba29e372e31a3de8"},"schema_version":"1.0"},"canonical_sha256":"d75ae5a38fe7c0149705e7da8265e8543cd2914472c5f6f92d2e75cd377479c2","source":{"kind":"arxiv","id":"1503.05433","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05433","created_at":"2026-05-18T00:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05433v3","created_at":"2026-05-18T00:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05433","created_at":"2026-05-18T00:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"25NOLI4P47AB","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"25NOLI4P47ABJFYF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"25NOLI4P","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:25NOLI4P47ABJFYF47NIEZPIKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05433","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-18T14:43:30Z","cross_cats_sorted":[],"title_canon_sha256":"bd20008423390d214d392137f3b3e32b2d2783ebbb277e6da460599f66fd100c","abstract_canon_sha256":"5ce9f40838e40617922003b0a0eee9958ca5233248b0dbd8ba29e372e31a3de8"},"schema_version":"1.0"},"canonical_sha256":"d75ae5a38fe7c0149705e7da8265e8543cd2914472c5f6f92d2e75cd377479c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:02.242893Z","signature_b64":"RPS2P3zCePmZtyj75an8n65WmPqWAlW357TH8MA5EThMV0+n360eBRtpDYAX+7eno3Xw9a/VnhfsAj51gxp4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d75ae5a38fe7c0149705e7da8265e8543cd2914472c5f6f92d2e75cd377479c2","last_reissued_at":"2026-05-18T00:17:02.242310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:02.242310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05433","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDwxUcozXNU2srkEV8MfHr1z79J1qC/Po8d9JMG6CPIVGsJji9xWu4oCegdDciPVl1jjJTwlKya+zZbBsVSBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:37:27.720630Z"},"content_sha256":"b0a87700c5808ecdb65c7cf254baf1198081f27687b61729c02adb8226b87fc0","schema_version":"1.0","event_id":"sha256:b0a87700c5808ecdb65c7cf254baf1198081f27687b61729c02adb8226b87fc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:25NOLI4P47ABJFYF47NIEZPIKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic and partial differential equations on non-smooth time-dependent domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Niklas L.P. Lundstr\\\"Om, Thomas \\\"Onskog","submitted_at":"2015-03-18T14:43:30Z","abstract_excerpt":"In this article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron's method, we also conclude existence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05433","kind":"arxiv","version":3},"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":"2026-05-18T00:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K1t/mdK+Lh2uYMU6cN5YKr0t1Z4KhC49QygdsVgGRv4CUN+mm/JsfVEql1Ag1gkMeexlx+dp2s7QWbRpI0ogAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:37:27.720977Z"},"content_sha256":"76ac9de33a970bf124b1b1ceb923bb96751bf57280bf9ec90d0501603846cb61","schema_version":"1.0","event_id":"sha256:76ac9de33a970bf124b1b1ceb923bb96751bf57280bf9ec90d0501603846cb61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25NOLI4P47ABJFYF47NIEZPIKQ/bundle.json","state_url":"https://pith.science/pith/25NOLI4P47ABJFYF47NIEZPIKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25NOLI4P47ABJFYF47NIEZPIKQ/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":"2026-06-22T17:37:27Z","links":{"resolver":"https://pith.science/pith/25NOLI4P47ABJFYF47NIEZPIKQ","bundle":"https://pith.science/pith/25NOLI4P47ABJFYF47NIEZPIKQ/bundle.json","state":"https://pith.science/pith/25NOLI4P47ABJFYF47NIEZPIKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25NOLI4P47ABJFYF47NIEZPIKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:25NOLI4P47ABJFYF47NIEZPIKQ","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":"5ce9f40838e40617922003b0a0eee9958ca5233248b0dbd8ba29e372e31a3de8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-18T14:43:30Z","title_canon_sha256":"bd20008423390d214d392137f3b3e32b2d2783ebbb277e6da460599f66fd100c"},"schema_version":"1.0","source":{"id":"1503.05433","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05433","created_at":"2026-05-18T00:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05433v3","created_at":"2026-05-18T00:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05433","created_at":"2026-05-18T00:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"25NOLI4P47AB","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"25NOLI4P47ABJFYF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"25NOLI4P","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:76ac9de33a970bf124b1b1ceb923bb96751bf57280bf9ec90d0501603846cb61","target":"graph","created_at":"2026-05-18T00:17:02Z","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 article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron's method, we also conclude existence ","authors_text":"Niklas L.P. Lundstr\\\"Om, Thomas \\\"Onskog","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-18T14:43:30Z","title":"Stochastic and partial differential equations on non-smooth time-dependent domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05433","kind":"arxiv","version":3},"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:b0a87700c5808ecdb65c7cf254baf1198081f27687b61729c02adb8226b87fc0","target":"record","created_at":"2026-05-18T00:17:02Z","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":"5ce9f40838e40617922003b0a0eee9958ca5233248b0dbd8ba29e372e31a3de8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-18T14:43:30Z","title_canon_sha256":"bd20008423390d214d392137f3b3e32b2d2783ebbb277e6da460599f66fd100c"},"schema_version":"1.0","source":{"id":"1503.05433","kind":"arxiv","version":3}},"canonical_sha256":"d75ae5a38fe7c0149705e7da8265e8543cd2914472c5f6f92d2e75cd377479c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75ae5a38fe7c0149705e7da8265e8543cd2914472c5f6f92d2e75cd377479c2","first_computed_at":"2026-05-18T00:17:02.242310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:02.242310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RPS2P3zCePmZtyj75an8n65WmPqWAlW357TH8MA5EThMV0+n360eBRtpDYAX+7eno3Xw9a/VnhfsAj51gxp4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:02.242893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05433","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0a87700c5808ecdb65c7cf254baf1198081f27687b61729c02adb8226b87fc0","sha256:76ac9de33a970bf124b1b1ceb923bb96751bf57280bf9ec90d0501603846cb61"],"state_sha256":"428717a34fcfa08636ddd708ff6f44ad6e29f59e668f8cd0a35aa2cf4982b631"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VnoIAutC52dT5aIYegusfVzVCOYnrxf+HcA/ojf2SBB1nulM/ZshGFUAv6cRZLdL0979x2roDtQyV1d2gIHfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:37:27.722964Z","bundle_sha256":"7fb55d9f1ed06cb2fda5cd06e47c03930abb0166bd002c2f43004618d1a83407"}}