{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ICSTEMKT3TOT5TEPTXEJ246BBS","short_pith_number":"pith:ICSTEMKT","canonical_record":{"source":{"id":"1311.4635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T07:21:35Z","cross_cats_sorted":[],"title_canon_sha256":"a4b585d275f03f5ac5cbfd341114d93e379acd64ef799834c184ea1aedd32176","abstract_canon_sha256":"958ddb2353c6a600bc746dd8ad0039b9f3527a34b9e4896df195b182ddc63b22"},"schema_version":"1.0"},"canonical_sha256":"40a5323153dcdd3ecc8f9dc89d73c10ca1d9c5e104c7e01ce061284c6c496f31","source":{"kind":"arxiv","id":"1311.4635","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4635","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4635v1","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4635","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"ICSTEMKT3TOT","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ICSTEMKT3TOT5TEP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ICSTEMKT","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ICSTEMKT3TOT5TEPTXEJ246BBS","target":"record","payload":{"canonical_record":{"source":{"id":"1311.4635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T07:21:35Z","cross_cats_sorted":[],"title_canon_sha256":"a4b585d275f03f5ac5cbfd341114d93e379acd64ef799834c184ea1aedd32176","abstract_canon_sha256":"958ddb2353c6a600bc746dd8ad0039b9f3527a34b9e4896df195b182ddc63b22"},"schema_version":"1.0"},"canonical_sha256":"40a5323153dcdd3ecc8f9dc89d73c10ca1d9c5e104c7e01ce061284c6c496f31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:23.254109Z","signature_b64":"NVH/fRmV3YlpmJtmfAAD6H6tuEUxgIxO+NSPpXCPtoMWy148blcQOYVXIfJlqv9GNAZZT+pa+I/xSpV6ox5WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40a5323153dcdd3ecc8f9dc89d73c10ca1d9c5e104c7e01ce061284c6c496f31","last_reissued_at":"2026-05-18T01:46:23.253561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:23.253561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.4635","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":"2026-05-18T01:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tN7lFD/TUWJIRv3pYxJaKNIwMcPQsHhwr5dlvtnROGG4BpC/h3KJLdx2v1dX+HqnBmIyThIF4Thm9fSgpnZiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:41:40.896138Z"},"content_sha256":"e8cde81c15a547111c8c24044ecf716a8cd27b4d421adec80c7e1927d31a2682","schema_version":"1.0","event_id":"sha256:e8cde81c15a547111c8c24044ecf716a8cd27b4d421adec80c7e1927d31a2682"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ICSTEMKT3TOT5TEPTXEJ246BBS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"THE Fokker-Planck Equation With Absorbing Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyung Ju Hwang, Juan J. L. Velazquez, Juhi Jang","submitted_at":"2013-11-19T07:21:35Z","abstract_excerpt":"We study the initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting solutions decay exponentially for long times. To prove these results we obtain several crucial estimates, which include hypoellipticity away from the singular set for the Fokker-Planck equation with absorbing boundary conditions, as well as the Holder continuity of the solutions up to the singular set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4635","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":"2026-05-18T01:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6Pn+EOKzo9tS+vZuhI5PufMwtVs2MMzNQrE0Bz7nZhM1mcykJW+MJatxH5PjWVMbTcj16lgSCDxxDaZjHZiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:41:40.896490Z"},"content_sha256":"c6c23b49c324b510487388989429a8a9f2b2046069690df7d5d68aaf9207f236","schema_version":"1.0","event_id":"sha256:c6c23b49c324b510487388989429a8a9f2b2046069690df7d5d68aaf9207f236"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ICSTEMKT3TOT5TEPTXEJ246BBS/bundle.json","state_url":"https://pith.science/pith/ICSTEMKT3TOT5TEPTXEJ246BBS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ICSTEMKT3TOT5TEPTXEJ246BBS/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":"2026-06-08T10:41:40Z","links":{"resolver":"https://pith.science/pith/ICSTEMKT3TOT5TEPTXEJ246BBS","bundle":"https://pith.science/pith/ICSTEMKT3TOT5TEPTXEJ246BBS/bundle.json","state":"https://pith.science/pith/ICSTEMKT3TOT5TEPTXEJ246BBS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ICSTEMKT3TOT5TEPTXEJ246BBS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ICSTEMKT3TOT5TEPTXEJ246BBS","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":"958ddb2353c6a600bc746dd8ad0039b9f3527a34b9e4896df195b182ddc63b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T07:21:35Z","title_canon_sha256":"a4b585d275f03f5ac5cbfd341114d93e379acd64ef799834c184ea1aedd32176"},"schema_version":"1.0","source":{"id":"1311.4635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4635","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4635v1","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4635","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"ICSTEMKT3TOT","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ICSTEMKT3TOT5TEP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ICSTEMKT","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:c6c23b49c324b510487388989429a8a9f2b2046069690df7d5d68aaf9207f236","target":"graph","created_at":"2026-05-18T01:46:23Z","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 initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting solutions decay exponentially for long times. To prove these results we obtain several crucial estimates, which include hypoellipticity away from the singular set for the Fokker-Planck equation with absorbing boundary conditions, as well as the Holder continuity of the solutions up to the singular set.","authors_text":"Hyung Ju Hwang, Juan J. L. Velazquez, Juhi Jang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T07:21:35Z","title":"THE Fokker-Planck Equation With Absorbing Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4635","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:e8cde81c15a547111c8c24044ecf716a8cd27b4d421adec80c7e1927d31a2682","target":"record","created_at":"2026-05-18T01:46:23Z","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":"958ddb2353c6a600bc746dd8ad0039b9f3527a34b9e4896df195b182ddc63b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T07:21:35Z","title_canon_sha256":"a4b585d275f03f5ac5cbfd341114d93e379acd64ef799834c184ea1aedd32176"},"schema_version":"1.0","source":{"id":"1311.4635","kind":"arxiv","version":1}},"canonical_sha256":"40a5323153dcdd3ecc8f9dc89d73c10ca1d9c5e104c7e01ce061284c6c496f31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40a5323153dcdd3ecc8f9dc89d73c10ca1d9c5e104c7e01ce061284c6c496f31","first_computed_at":"2026-05-18T01:46:23.253561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:23.253561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NVH/fRmV3YlpmJtmfAAD6H6tuEUxgIxO+NSPpXCPtoMWy148blcQOYVXIfJlqv9GNAZZT+pa+I/xSpV6ox5WDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:23.254109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8cde81c15a547111c8c24044ecf716a8cd27b4d421adec80c7e1927d31a2682","sha256:c6c23b49c324b510487388989429a8a9f2b2046069690df7d5d68aaf9207f236"],"state_sha256":"9ad13a3476396bb5796999b7596270b53445f5bcf74f0be7ef22a10bc721ba9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"guBXOAzG8cm18/P9BkB9/1Dk7VyzHYOYZYlC+F3gStvXKuszsFhOMs3u0PEG4rgxL9kz4tyr6L89W5L0H68NCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:41:40.898405Z","bundle_sha256":"c49db84d57b806f5d41a15dc6a2d57375d6d8262eb13df21a6d4756ffd6d3e40"}}