{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KZS7SPJHOJQODBDH2QZ64TZDM6","short_pith_number":"pith:KZS7SPJH","canonical_record":{"source":{"id":"1301.5795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-24T14:37:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"09c37977bebc1f7f99221ef1de11c7f9913b8c2ef127d5627c5809ca116bead9","abstract_canon_sha256":"9537e223343a9837c53128017fc66e4df4184c72e66391f9b3dd24607ca312ff"},"schema_version":"1.0"},"canonical_sha256":"5665f93d277260e18467d433ee4f2367b509cd7463a6c2d385cde9817a916124","source":{"kind":"arxiv","id":"1301.5795","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5795","created_at":"2026-05-18T01:36:26Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5795v2","created_at":"2026-05-18T01:36:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5795","created_at":"2026-05-18T01:36:26Z"},{"alias_kind":"pith_short_12","alias_value":"KZS7SPJHOJQO","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KZS7SPJHOJQODBDH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KZS7SPJH","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KZS7SPJHOJQODBDH2QZ64TZDM6","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-24T14:37:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"09c37977bebc1f7f99221ef1de11c7f9913b8c2ef127d5627c5809ca116bead9","abstract_canon_sha256":"9537e223343a9837c53128017fc66e4df4184c72e66391f9b3dd24607ca312ff"},"schema_version":"1.0"},"canonical_sha256":"5665f93d277260e18467d433ee4f2367b509cd7463a6c2d385cde9817a916124","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:26.088806Z","signature_b64":"eNrwGLZCsDjhCEkD8owxaBQ8yVD3AvP46d+Jk2J2oZe1owMG/d2U+mbhXMLxMXArMTp3r7Q1w0i3AkFulWsHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5665f93d277260e18467d433ee4f2367b509cd7463a6c2d385cde9817a916124","last_reissued_at":"2026-05-18T01:36:26.088439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:26.088439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5795","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHA/sHbT/LY2IzBs8M9briyfMbJFOWTKXHvs5oEuxPfUQzod4Dcanq5sLhO4iKODZd+0maY55+ghG8ruvncKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:08:34.362722Z"},"content_sha256":"6b9fad2a316de116bd62e7c3443875ec099261fb6a51f97c494802be26498eb7","schema_version":"1.0","event_id":"sha256:6b9fad2a316de116bd62e7c3443875ec099261fb6a51f97c494802be26498eb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KZS7SPJHOJQODBDH2QZ64TZDM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obstacle problem for semilinear parabolic equations with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Andrzej Rozkosz, Tomasz Klimsiak","submitted_at":"2013-01-24T14:37:22Z","abstract_excerpt":"We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem and well as results on approximation of the solutions by the penaliztion method. In the proofs we use probabilistic methods of the theory of Markov processes and the theory of backward stochastic differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5795","kind":"arxiv","version":2},"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":"2026-05-18T01:36:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KPRnW9uuP/O5A6TvTxcDsAwiYCW15Jh4lSLMosqCFw4NIsGzdM7DF0iMHLAwXtsL8/a1Dx2QDOLCqkiV3qMEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:08:34.363061Z"},"content_sha256":"9c2240e0357ac33e4980701ef7bbd0de3423f423a51ec0300060a03e00d021f7","schema_version":"1.0","event_id":"sha256:9c2240e0357ac33e4980701ef7bbd0de3423f423a51ec0300060a03e00d021f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZS7SPJHOJQODBDH2QZ64TZDM6/bundle.json","state_url":"https://pith.science/pith/KZS7SPJHOJQODBDH2QZ64TZDM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZS7SPJHOJQODBDH2QZ64TZDM6/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":"2026-06-27T16:08:34Z","links":{"resolver":"https://pith.science/pith/KZS7SPJHOJQODBDH2QZ64TZDM6","bundle":"https://pith.science/pith/KZS7SPJHOJQODBDH2QZ64TZDM6/bundle.json","state":"https://pith.science/pith/KZS7SPJHOJQODBDH2QZ64TZDM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZS7SPJHOJQODBDH2QZ64TZDM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KZS7SPJHOJQODBDH2QZ64TZDM6","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":"9537e223343a9837c53128017fc66e4df4184c72e66391f9b3dd24607ca312ff","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-24T14:37:22Z","title_canon_sha256":"09c37977bebc1f7f99221ef1de11c7f9913b8c2ef127d5627c5809ca116bead9"},"schema_version":"1.0","source":{"id":"1301.5795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5795","created_at":"2026-05-18T01:36:26Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5795v2","created_at":"2026-05-18T01:36:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5795","created_at":"2026-05-18T01:36:26Z"},{"alias_kind":"pith_short_12","alias_value":"KZS7SPJHOJQO","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KZS7SPJHOJQODBDH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KZS7SPJH","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:9c2240e0357ac33e4980701ef7bbd0de3423f423a51ec0300060a03e00d021f7","target":"graph","created_at":"2026-05-18T01:36:26Z","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 consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem and well as results on approximation of the solutions by the penaliztion method. In the proofs we use probabilistic methods of the theory of Markov processes and the theory of backward stochastic differential equations.","authors_text":"Andrzej Rozkosz, Tomasz Klimsiak","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-24T14:37:22Z","title":"Obstacle problem for semilinear parabolic equations with measure data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5795","kind":"arxiv","version":2},"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":"sha256:6b9fad2a316de116bd62e7c3443875ec099261fb6a51f97c494802be26498eb7","target":"record","created_at":"2026-05-18T01:36:26Z","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":"9537e223343a9837c53128017fc66e4df4184c72e66391f9b3dd24607ca312ff","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-24T14:37:22Z","title_canon_sha256":"09c37977bebc1f7f99221ef1de11c7f9913b8c2ef127d5627c5809ca116bead9"},"schema_version":"1.0","source":{"id":"1301.5795","kind":"arxiv","version":2}},"canonical_sha256":"5665f93d277260e18467d433ee4f2367b509cd7463a6c2d385cde9817a916124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5665f93d277260e18467d433ee4f2367b509cd7463a6c2d385cde9817a916124","first_computed_at":"2026-05-18T01:36:26.088439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:26.088439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNrwGLZCsDjhCEkD8owxaBQ8yVD3AvP46d+Jk2J2oZe1owMG/d2U+mbhXMLxMXArMTp3r7Q1w0i3AkFulWsHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:26.088806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b9fad2a316de116bd62e7c3443875ec099261fb6a51f97c494802be26498eb7","sha256:9c2240e0357ac33e4980701ef7bbd0de3423f423a51ec0300060a03e00d021f7"],"state_sha256":"c1d7e1a1e65fe8c53a8ef777f4d31fabfa201c8b90dd571618774df7d29d199e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nj/gMY6WLXkOYcsZ8iTYq5BaB1TtMmoGAR9fc97Zayd5+Vm4LX2efQGzx4kC8rwNKUBINXT4N8AtVWZaEaGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:08:34.364989Z","bundle_sha256":"510ddc70fa86324f49c42152e176083af3b0b44c83978127460155d56bc5b50f"}}