{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PFSOFVGXAQJ27SDGNZDXDE4V5C","short_pith_number":"pith:PFSOFVGX","canonical_record":{"source":{"id":"1608.02044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-06T00:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"edc24844a02b28315cad51560c6a20f05e39d3939261df9512cfe22ed31b0609","abstract_canon_sha256":"52a997350a4d8bb0012bcea82c915076a094a0db1f5b83cb82289070319b0aca"},"schema_version":"1.0"},"canonical_sha256":"7964e2d4d70413afc8666e47719395e8a5acfbe89378f563e37594cd529c203c","source":{"kind":"arxiv","id":"1608.02044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02044","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02044v2","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02044","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"PFSOFVGXAQJ2","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFSOFVGXAQJ27SDG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFSOFVGX","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PFSOFVGXAQJ27SDGNZDXDE4V5C","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-06T00:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"edc24844a02b28315cad51560c6a20f05e39d3939261df9512cfe22ed31b0609","abstract_canon_sha256":"52a997350a4d8bb0012bcea82c915076a094a0db1f5b83cb82289070319b0aca"},"schema_version":"1.0"},"canonical_sha256":"7964e2d4d70413afc8666e47719395e8a5acfbe89378f563e37594cd529c203c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:07.182107Z","signature_b64":"91Jt3Zb/QHVFo4wji+1OeEiYMA9n79d0h18hQ9ZYaJcK+VnSDJs4fLtRTsTqgFzyN8oY8RyC1MZ8QpCR/4jOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7964e2d4d70413afc8666e47719395e8a5acfbe89378f563e37594cd529c203c","last_reissued_at":"2026-05-18T00:51:07.181676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:07.181676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02044","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":"2026-05-18T00:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G2f0W+iUryEm4Z/J/IdW+v+Q//H1/Khiumi0SL5GHuWoc5V12BAGWcjDbBkCBDtervN1bqyZz3FcUlEmMXs2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:57:27.687837Z"},"content_sha256":"908ee26cbbd06c64a4d468dd689d2c265a6df33741c68da17a8f34996dcbca6b","schema_version":"1.0","event_id":"sha256:908ee26cbbd06c64a4d468dd689d2c265a6df33741c68da17a8f34996dcbca6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PFSOFVGXAQJ27SDGNZDXDE4V5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camelia A. Pop, Charles L. Epstein","submitted_at":"2016-08-06T00:32:19Z","abstract_excerpt":"We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy homogeneous Dirichlet boundary conditions on certain portions of the boundary. Such equations arise in population genetics in the study of models for the evolution of gene frequencies. Among the applications of our results is the description of the structure of the transition probabilities and of the hitting distributions of the underlying gene frequencies process"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02044","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":"2026-05-18T00:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbSmar5g121uQbO0y+AWuXH4ZzQqYyxpwydVc83OIcO0j1TIylr7MP/BqZTNTJhkvVoBpYccBxqDf1IB29p8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:57:27.688185Z"},"content_sha256":"09423f03d8007e5f7ffd26a285249ddf040ad540ec875ed6ab904b7164c1e386","schema_version":"1.0","event_id":"sha256:09423f03d8007e5f7ffd26a285249ddf040ad540ec875ed6ab904b7164c1e386"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C/bundle.json","state_url":"https://pith.science/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C/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":"2026-06-03T10:57:27Z","links":{"resolver":"https://pith.science/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C","bundle":"https://pith.science/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C/bundle.json","state":"https://pith.science/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFSOFVGXAQJ27SDGNZDXDE4V5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PFSOFVGXAQJ27SDGNZDXDE4V5C","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":"52a997350a4d8bb0012bcea82c915076a094a0db1f5b83cb82289070319b0aca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-06T00:32:19Z","title_canon_sha256":"edc24844a02b28315cad51560c6a20f05e39d3939261df9512cfe22ed31b0609"},"schema_version":"1.0","source":{"id":"1608.02044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02044","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02044v2","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02044","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"PFSOFVGXAQJ2","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFSOFVGXAQJ27SDG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFSOFVGX","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:09423f03d8007e5f7ffd26a285249ddf040ad540ec875ed6ab904b7164c1e386","target":"graph","created_at":"2026-05-18T00:51:07Z","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 boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy homogeneous Dirichlet boundary conditions on certain portions of the boundary. Such equations arise in population genetics in the study of models for the evolution of gene frequencies. Among the applications of our results is the description of the structure of the transition probabilities and of the hitting distributions of the underlying gene frequencies process","authors_text":"Camelia A. Pop, Charles L. Epstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-06T00:32:19Z","title":"Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02044","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":"sha256:908ee26cbbd06c64a4d468dd689d2c265a6df33741c68da17a8f34996dcbca6b","target":"record","created_at":"2026-05-18T00:51:07Z","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":"52a997350a4d8bb0012bcea82c915076a094a0db1f5b83cb82289070319b0aca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-06T00:32:19Z","title_canon_sha256":"edc24844a02b28315cad51560c6a20f05e39d3939261df9512cfe22ed31b0609"},"schema_version":"1.0","source":{"id":"1608.02044","kind":"arxiv","version":2}},"canonical_sha256":"7964e2d4d70413afc8666e47719395e8a5acfbe89378f563e37594cd529c203c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7964e2d4d70413afc8666e47719395e8a5acfbe89378f563e37594cd529c203c","first_computed_at":"2026-05-18T00:51:07.181676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:07.181676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"91Jt3Zb/QHVFo4wji+1OeEiYMA9n79d0h18hQ9ZYaJcK+VnSDJs4fLtRTsTqgFzyN8oY8RyC1MZ8QpCR/4jOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:07.182107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:908ee26cbbd06c64a4d468dd689d2c265a6df33741c68da17a8f34996dcbca6b","sha256:09423f03d8007e5f7ffd26a285249ddf040ad540ec875ed6ab904b7164c1e386"],"state_sha256":"67b1ad3eccb57a2f9d1c642947e2a14b9dfd597c07d9719b4f2564eb39777857"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hK8Y8G3UCsPznI+/YUTOip5L6qMiuDSvWkcLGUkESf1nWZV4YqIAX/3POP7vyxvBf5/ZYl5Zrr8javTlef/DDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:57:27.690140Z","bundle_sha256":"997f4e58ef622ba486c7bca71bea0116f5625e4362afc9c6bbb6634165d40077"}}