{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LTJE6EYC26K7MJKNJWERLIAAR2","short_pith_number":"pith:LTJE6EYC","canonical_record":{"source":{"id":"1606.07133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T22:44:04Z","cross_cats_sorted":[],"title_canon_sha256":"ee4ebe3ee6cb1412a99302fc1091931385875bbda9cb49d9c3ab10b3e2be5df9","abstract_canon_sha256":"367cd167045deacad21e6c54d29d8baa50c1366ece8951e0e2f402076bfa95a2"},"schema_version":"1.0"},"canonical_sha256":"5cd24f1302d795f6254d4d8915a0008e82b70501c4315c71d0a596510b72cf51","source":{"kind":"arxiv","id":"1606.07133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07133","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07133v1","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07133","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"LTJE6EYC26K7","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LTJE6EYC26K7MJKN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LTJE6EYC","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LTJE6EYC26K7MJKNJWERLIAAR2","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T22:44:04Z","cross_cats_sorted":[],"title_canon_sha256":"ee4ebe3ee6cb1412a99302fc1091931385875bbda9cb49d9c3ab10b3e2be5df9","abstract_canon_sha256":"367cd167045deacad21e6c54d29d8baa50c1366ece8951e0e2f402076bfa95a2"},"schema_version":"1.0"},"canonical_sha256":"5cd24f1302d795f6254d4d8915a0008e82b70501c4315c71d0a596510b72cf51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:58.610553Z","signature_b64":"EMiqP2ppRcqzfLuDjHnXJvBJHQzjhl+fZULcKyzoYwggISH8NuFLBS0jAtmKnYrMATrDKS3/JPljFNxgRyy5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cd24f1302d795f6254d4d8915a0008e82b70501c4315c71d0a596510b72cf51","last_reissued_at":"2026-05-18T01:11:58.610217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:58.610217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07133","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":"2026-05-18T01:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBMLBk+qoHL/7Pt8rvgLR4iDeoB1R2t7GfmvZ6+4QUmwsMbgd0zLjTX/pgn+l3WfdEU9sqVYnmA+/WQzLn7HDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:10:48.640478Z"},"content_sha256":"e052b60505b6d97d649db6185ccd51aa92b1e0e15bbebb18fb454d7d3015d5e0","schema_version":"1.0","event_id":"sha256:e052b60505b6d97d649db6185ccd51aa92b1e0e15bbebb18fb454d7d3015d5e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LTJE6EYC26K7MJKNJWERLIAAR2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Dirichlet Problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessia E. Kogoj","submitted_at":"2016-06-22T22:44:04Z","abstract_excerpt":"We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient condition for the regularity of the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07133","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":"2026-05-18T01:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sc1sE8OcA4vTf/Ulko/eM3jmLypN4jEzsenRAMqLTKauasz+LCxmJXQ6ZE62sqCJKEh+b2UKRdYZAZ3HlfouBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:10:48.640816Z"},"content_sha256":"e67f519107045c71ae8fdc0fdc8f38df2190a0555f64d7c8168821af233e126d","schema_version":"1.0","event_id":"sha256:e67f519107045c71ae8fdc0fdc8f38df2190a0555f64d7c8168821af233e126d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTJE6EYC26K7MJKNJWERLIAAR2/bundle.json","state_url":"https://pith.science/pith/LTJE6EYC26K7MJKNJWERLIAAR2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTJE6EYC26K7MJKNJWERLIAAR2/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":"2026-06-20T22:10:48Z","links":{"resolver":"https://pith.science/pith/LTJE6EYC26K7MJKNJWERLIAAR2","bundle":"https://pith.science/pith/LTJE6EYC26K7MJKNJWERLIAAR2/bundle.json","state":"https://pith.science/pith/LTJE6EYC26K7MJKNJWERLIAAR2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTJE6EYC26K7MJKNJWERLIAAR2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LTJE6EYC26K7MJKNJWERLIAAR2","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":"367cd167045deacad21e6c54d29d8baa50c1366ece8951e0e2f402076bfa95a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T22:44:04Z","title_canon_sha256":"ee4ebe3ee6cb1412a99302fc1091931385875bbda9cb49d9c3ab10b3e2be5df9"},"schema_version":"1.0","source":{"id":"1606.07133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07133","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07133v1","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07133","created_at":"2026-05-18T01:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"LTJE6EYC26K7","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LTJE6EYC26K7MJKN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LTJE6EYC","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:e67f519107045c71ae8fdc0fdc8f38df2190a0555f64d7c8168821af233e126d","target":"graph","created_at":"2026-05-18T01:11:58Z","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 show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient condition for the regularity of the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan.","authors_text":"Alessia E. Kogoj","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T22:44:04Z","title":"On the Dirichlet Problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07133","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:e052b60505b6d97d649db6185ccd51aa92b1e0e15bbebb18fb454d7d3015d5e0","target":"record","created_at":"2026-05-18T01:11:58Z","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":"367cd167045deacad21e6c54d29d8baa50c1366ece8951e0e2f402076bfa95a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-22T22:44:04Z","title_canon_sha256":"ee4ebe3ee6cb1412a99302fc1091931385875bbda9cb49d9c3ab10b3e2be5df9"},"schema_version":"1.0","source":{"id":"1606.07133","kind":"arxiv","version":1}},"canonical_sha256":"5cd24f1302d795f6254d4d8915a0008e82b70501c4315c71d0a596510b72cf51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cd24f1302d795f6254d4d8915a0008e82b70501c4315c71d0a596510b72cf51","first_computed_at":"2026-05-18T01:11:58.610217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:58.610217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EMiqP2ppRcqzfLuDjHnXJvBJHQzjhl+fZULcKyzoYwggISH8NuFLBS0jAtmKnYrMATrDKS3/JPljFNxgRyy5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:58.610553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e052b60505b6d97d649db6185ccd51aa92b1e0e15bbebb18fb454d7d3015d5e0","sha256:e67f519107045c71ae8fdc0fdc8f38df2190a0555f64d7c8168821af233e126d"],"state_sha256":"5e4277c778da5024cf1298071a5522a6c90c7e1b4db7d6cd1623557fb9d851d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dk1rhsZVcu8TsDagnIl/yUeNvgtbR3twaMEAFWGtclvLlw1dV4RLYHMUnrXSSYheVTpo0C3bxW/YkEXP0gjQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:10:48.642694Z","bundle_sha256":"9ab7656f37526ce4602638a9d69d5a93d873ed8ced0b060ca664eb7fa65c0bbb"}}