{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RI63PMJYUNY6DC2FZW4OJYVIU7","short_pith_number":"pith:RI63PMJY","canonical_record":{"source":{"id":"1803.10641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T14:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"3cea6d784fdc0e5ed2a3f3817170036adea669b265d5f1491bc0e813ffa6d3db","abstract_canon_sha256":"8e672afcd12743684d39d8be1e17c5a5355117e5a7d5e26d3c3277d24ec5c46e"},"schema_version":"1.0"},"canonical_sha256":"8a3db7b138a371e18b45cdb8e4e2a8a7ea7d104a50776db767f57a769ef5e0eb","source":{"kind":"arxiv","id":"1803.10641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10641","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10641v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10641","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"RI63PMJYUNY6","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RI63PMJYUNY6DC2F","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RI63PMJY","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RI63PMJYUNY6DC2FZW4OJYVIU7","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T14:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"3cea6d784fdc0e5ed2a3f3817170036adea669b265d5f1491bc0e813ffa6d3db","abstract_canon_sha256":"8e672afcd12743684d39d8be1e17c5a5355117e5a7d5e26d3c3277d24ec5c46e"},"schema_version":"1.0"},"canonical_sha256":"8a3db7b138a371e18b45cdb8e4e2a8a7ea7d104a50776db767f57a769ef5e0eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:54.611175Z","signature_b64":"faG2bVJjivrEzwXdw/B51dVJzPx+OTsOZleEaqsCzD2p/+Ly3JTmLq8UD1lNhpAlG3ao7vC74B/4u+Y9FS8wAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a3db7b138a371e18b45cdb8e4e2a8a7ea7d104a50776db767f57a769ef5e0eb","last_reissued_at":"2026-05-18T00:19:54.610392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:54.610392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10641","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":"2026-05-18T00:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjJXk8918tArWHk/1JrzlqRNLm9b2d4ETbVKd55X4TU4lBBMQY1clyUgQg7KyT7oKX1jwlhJKmVE5+ynf4bFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:17:04.295654Z"},"content_sha256":"61a53bd0a948d9ef9137b6a1175ff7599b64f8b8f4a702602b5aaac83be1edc8","schema_version":"1.0","event_id":"sha256:61a53bd0a948d9ef9137b6a1175ff7599b64f8b8f4a702602b5aaac83be1edc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RI63PMJYUNY6DC2FZW4OJYVIU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary regularity for a degenerate elliptic equation with mixed boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alassane Niang","submitted_at":"2018-03-28T14:25:30Z","abstract_excerpt":"We consider a function U satisfying a degenerate elliptic equation on (0,+\\infty)\\times R^N with mixed Dirichlet-Neumann boundary conditions. The Neumann condition is prescribed on a bounded domain \\Omega\\subset R^N of class C^{1;1}, whereas the Dirichlet data is on the exterior of \\Omega. We prove Holder regularity estimates of U/d^s, where d is a distance function defined as d(z) := dist(z;R^N\\setminus\\Omega), for z\\in (0,+\\infty)\\times R^N. The degenerate elliptic equation arises from the Caffarelli-Silvestre extension of the Dirichlet problem for the fractional Laplacian. Our proof relies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10641","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":"2026-05-18T00:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTpqhMxA8gcLmmHtUwnJN2dIb5YU4vczheHWqW3WFzY+aOzT2uLcAZ4SrSYFmeVR3D/icvtFMyFnWuQqBnYbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:17:04.296300Z"},"content_sha256":"1def9bb96d81367dcda3f4d93b047464f0364656a4f578aad89b87b1dc7e6132","schema_version":"1.0","event_id":"sha256:1def9bb96d81367dcda3f4d93b047464f0364656a4f578aad89b87b1dc7e6132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RI63PMJYUNY6DC2FZW4OJYVIU7/bundle.json","state_url":"https://pith.science/pith/RI63PMJYUNY6DC2FZW4OJYVIU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RI63PMJYUNY6DC2FZW4OJYVIU7/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":"2026-05-27T12:17:04Z","links":{"resolver":"https://pith.science/pith/RI63PMJYUNY6DC2FZW4OJYVIU7","bundle":"https://pith.science/pith/RI63PMJYUNY6DC2FZW4OJYVIU7/bundle.json","state":"https://pith.science/pith/RI63PMJYUNY6DC2FZW4OJYVIU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RI63PMJYUNY6DC2FZW4OJYVIU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RI63PMJYUNY6DC2FZW4OJYVIU7","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":"8e672afcd12743684d39d8be1e17c5a5355117e5a7d5e26d3c3277d24ec5c46e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T14:25:30Z","title_canon_sha256":"3cea6d784fdc0e5ed2a3f3817170036adea669b265d5f1491bc0e813ffa6d3db"},"schema_version":"1.0","source":{"id":"1803.10641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10641","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10641v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10641","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"RI63PMJYUNY6","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RI63PMJYUNY6DC2F","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RI63PMJY","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:1def9bb96d81367dcda3f4d93b047464f0364656a4f578aad89b87b1dc7e6132","target":"graph","created_at":"2026-05-18T00:19:54Z","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 a function U satisfying a degenerate elliptic equation on (0,+\\infty)\\times R^N with mixed Dirichlet-Neumann boundary conditions. The Neumann condition is prescribed on a bounded domain \\Omega\\subset R^N of class C^{1;1}, whereas the Dirichlet data is on the exterior of \\Omega. We prove Holder regularity estimates of U/d^s, where d is a distance function defined as d(z) := dist(z;R^N\\setminus\\Omega), for z\\in (0,+\\infty)\\times R^N. The degenerate elliptic equation arises from the Caffarelli-Silvestre extension of the Dirichlet problem for the fractional Laplacian. Our proof relies","authors_text":"Alassane Niang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T14:25:30Z","title":"Boundary regularity for a degenerate elliptic equation with mixed boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10641","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":"sha256:61a53bd0a948d9ef9137b6a1175ff7599b64f8b8f4a702602b5aaac83be1edc8","target":"record","created_at":"2026-05-18T00:19:54Z","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":"8e672afcd12743684d39d8be1e17c5a5355117e5a7d5e26d3c3277d24ec5c46e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T14:25:30Z","title_canon_sha256":"3cea6d784fdc0e5ed2a3f3817170036adea669b265d5f1491bc0e813ffa6d3db"},"schema_version":"1.0","source":{"id":"1803.10641","kind":"arxiv","version":1}},"canonical_sha256":"8a3db7b138a371e18b45cdb8e4e2a8a7ea7d104a50776db767f57a769ef5e0eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a3db7b138a371e18b45cdb8e4e2a8a7ea7d104a50776db767f57a769ef5e0eb","first_computed_at":"2026-05-18T00:19:54.610392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:54.610392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"faG2bVJjivrEzwXdw/B51dVJzPx+OTsOZleEaqsCzD2p/+Ly3JTmLq8UD1lNhpAlG3ao7vC74B/4u+Y9FS8wAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:54.611175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61a53bd0a948d9ef9137b6a1175ff7599b64f8b8f4a702602b5aaac83be1edc8","sha256:1def9bb96d81367dcda3f4d93b047464f0364656a4f578aad89b87b1dc7e6132"],"state_sha256":"3ddcc744a9d1e85608aff0c9e7769302df38fa4e60038658bde72ed30a5167c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mfRpFKoLINyX5AMY7Sf/eE8H+SB9VBk5Ygbzt5Sdg4eONb51gc7sCZ7jBmI3Z+Ku52iiy7riYpSuIKQ8CHa7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:17:04.299628Z","bundle_sha256":"9c9d000d165e5a12b82b2a1361334717f7f47f4acbb22eaecc9aff92c4642bd7"}}