{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HPF6F5GX5AOR36HA2BJR6WXDVN","short_pith_number":"pith:HPF6F5GX","canonical_record":{"source":{"id":"1804.01716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T08:06:56Z","cross_cats_sorted":[],"title_canon_sha256":"6438699be1e4c5103d1be38900d96cb9d20f85615516fe1791b1676a70551380","abstract_canon_sha256":"9dc68938fc94b8d5bf3335231bb49ce4bcdf2bb63f5ee9a2a643bc4ef3d6d227"},"schema_version":"1.0"},"canonical_sha256":"3bcbe2f4d7e81d1df8e0d0531f5ae3ab4843d42313c8f449f8ed70292f99fe93","source":{"kind":"arxiv","id":"1804.01716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01716","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01716v1","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01716","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"HPF6F5GX5AOR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HPF6F5GX5AOR36HA","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HPF6F5GX","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HPF6F5GX5AOR36HA2BJR6WXDVN","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T08:06:56Z","cross_cats_sorted":[],"title_canon_sha256":"6438699be1e4c5103d1be38900d96cb9d20f85615516fe1791b1676a70551380","abstract_canon_sha256":"9dc68938fc94b8d5bf3335231bb49ce4bcdf2bb63f5ee9a2a643bc4ef3d6d227"},"schema_version":"1.0"},"canonical_sha256":"3bcbe2f4d7e81d1df8e0d0531f5ae3ab4843d42313c8f449f8ed70292f99fe93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:10.208408Z","signature_b64":"5Ki7l5eSBc2xk1l6KvxGbs5ORf10xt+G2Lr82K0kzHy2GCyt8/ZPrLEzUqXjU+4KRO2mqUxOYbsEzZAK3gvKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bcbe2f4d7e81d1df8e0d0531f5ae3ab4843d42313c8f449f8ed70292f99fe93","last_reissued_at":"2026-05-18T00:19:10.207715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:10.207715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01716","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":"2026-05-18T00:19:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkh0nGqPgXkJnxnKkyXUYlkLqAaJZJy0ERUOuNmfRUuVLfQYhSibU4d5lt7RFwzvZinXRXee3CKB3ebcwuFmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:12:56.908215Z"},"content_sha256":"9918001e18dc8c967208e27a1561968cc53551f90a2d5cd096085830aa43a469","schema_version":"1.0","event_id":"sha256:9918001e18dc8c967208e27a1561968cc53551f90a2d5cd096085830aa43a469"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HPF6F5GX5AOR36HA2BJR6WXDVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary regularity for nonlocal operators with kernels of variable orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaehun Lee, Ki-Ahm Lee, Minhyun Kim, Panki Kim","submitted_at":"2018-04-05T08:06:56Z","abstract_excerpt":"We study the boundary regularity of solutions of the Dirichlet problem for the nonlocal operator with a kernel of variable orders. Since the order of differentiability of the kernel is not represented by a single number, we consider the generalized H\\\"older space. We prove that there exists a unique viscosity solution of $Lu = f$ in $D$, $u=0$ in $\\mathbb{R}^n \\setminus D$, where $D$ is a bounded $C^{1,1}$ open set, and that the solution $u$ satisfies $u \\in C^V(D)$ and $u/V(d_D) \\in C^\\alpha (D)$ with the uniform estimates, where $V$ is the renewal function and $d_D(x) = \\mbox{dist}(x, \\parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01716","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":"2026-05-18T00:19:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p00lzZjavMrB8KJY6fqv608JnxsIY5lWaGfIzJrh12bCVgqn+po4nPhZRv/NQ0aLh4W5Aa1fjnXfkGpfl+U8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:12:56.908576Z"},"content_sha256":"6febe352b9a612b566c009f192e113ad1e083452135a2ecb7de62df2efb8eead","schema_version":"1.0","event_id":"sha256:6febe352b9a612b566c009f192e113ad1e083452135a2ecb7de62df2efb8eead"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPF6F5GX5AOR36HA2BJR6WXDVN/bundle.json","state_url":"https://pith.science/pith/HPF6F5GX5AOR36HA2BJR6WXDVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPF6F5GX5AOR36HA2BJR6WXDVN/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":"2026-07-02T15:12:56Z","links":{"resolver":"https://pith.science/pith/HPF6F5GX5AOR36HA2BJR6WXDVN","bundle":"https://pith.science/pith/HPF6F5GX5AOR36HA2BJR6WXDVN/bundle.json","state":"https://pith.science/pith/HPF6F5GX5AOR36HA2BJR6WXDVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPF6F5GX5AOR36HA2BJR6WXDVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HPF6F5GX5AOR36HA2BJR6WXDVN","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":"9dc68938fc94b8d5bf3335231bb49ce4bcdf2bb63f5ee9a2a643bc4ef3d6d227","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T08:06:56Z","title_canon_sha256":"6438699be1e4c5103d1be38900d96cb9d20f85615516fe1791b1676a70551380"},"schema_version":"1.0","source":{"id":"1804.01716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01716","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01716v1","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01716","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"HPF6F5GX5AOR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HPF6F5GX5AOR36HA","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HPF6F5GX","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:6febe352b9a612b566c009f192e113ad1e083452135a2ecb7de62df2efb8eead","target":"graph","created_at":"2026-05-18T00:19:10Z","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 of solutions of the Dirichlet problem for the nonlocal operator with a kernel of variable orders. Since the order of differentiability of the kernel is not represented by a single number, we consider the generalized H\\\"older space. We prove that there exists a unique viscosity solution of $Lu = f$ in $D$, $u=0$ in $\\mathbb{R}^n \\setminus D$, where $D$ is a bounded $C^{1,1}$ open set, and that the solution $u$ satisfies $u \\in C^V(D)$ and $u/V(d_D) \\in C^\\alpha (D)$ with the uniform estimates, where $V$ is the renewal function and $d_D(x) = \\mbox{dist}(x, \\parti","authors_text":"Jaehun Lee, Ki-Ahm Lee, Minhyun Kim, Panki Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T08:06:56Z","title":"Boundary regularity for nonlocal operators with kernels of variable orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01716","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":"sha256:9918001e18dc8c967208e27a1561968cc53551f90a2d5cd096085830aa43a469","target":"record","created_at":"2026-05-18T00:19:10Z","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":"9dc68938fc94b8d5bf3335231bb49ce4bcdf2bb63f5ee9a2a643bc4ef3d6d227","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T08:06:56Z","title_canon_sha256":"6438699be1e4c5103d1be38900d96cb9d20f85615516fe1791b1676a70551380"},"schema_version":"1.0","source":{"id":"1804.01716","kind":"arxiv","version":1}},"canonical_sha256":"3bcbe2f4d7e81d1df8e0d0531f5ae3ab4843d42313c8f449f8ed70292f99fe93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bcbe2f4d7e81d1df8e0d0531f5ae3ab4843d42313c8f449f8ed70292f99fe93","first_computed_at":"2026-05-18T00:19:10.207715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:10.207715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Ki7l5eSBc2xk1l6KvxGbs5ORf10xt+G2Lr82K0kzHy2GCyt8/ZPrLEzUqXjU+4KRO2mqUxOYbsEzZAK3gvKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:10.208408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9918001e18dc8c967208e27a1561968cc53551f90a2d5cd096085830aa43a469","sha256:6febe352b9a612b566c009f192e113ad1e083452135a2ecb7de62df2efb8eead"],"state_sha256":"a3300df2d9f7f8191b19f396ce2c4392b1d05ee7a98bc39527dea9d769b81a73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bWipaFKza0MuZIiRLmEwEgFyACulbt2h9DdYYBA/pTH/JQPescg5467my1q8M3CjBYullBkiqF6OYw0871qBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T15:12:56.910413Z","bundle_sha256":"a954c86da2b71cc0cfa6001ade0ca7efdd027b97093a083d208be598f75a9958"}}