{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UMLA5XQIN4DKONIF6KJFS3BCE3","short_pith_number":"pith:UMLA5XQI","canonical_record":{"source":{"id":"2406.05994","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-10T03:26:54Z","cross_cats_sorted":[],"title_canon_sha256":"40480a6e37f0e0afba7aef42048f15d90082ffc94b065b658a198ee99cddb263","abstract_canon_sha256":"5d0233b6de0eaf4d01fb90b0b9ec16c9916ddaf2dbfe984465621081959d60fa"},"schema_version":"1.0"},"canonical_sha256":"a3160ede086f06a73505f292596c2226fff52f5d4cc68ba9f3109b207384c60e","source":{"kind":"arxiv","id":"2406.05994","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.05994","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"2406.05994v3","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.05994","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"UMLA5XQIN4DK","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"pith_short_16","alias_value":"UMLA5XQIN4DKONIF","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"pith_short_8","alias_value":"UMLA5XQI","created_at":"2026-07-05T10:19:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UMLA5XQIN4DKONIF6KJFS3BCE3","target":"record","payload":{"canonical_record":{"source":{"id":"2406.05994","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-10T03:26:54Z","cross_cats_sorted":[],"title_canon_sha256":"40480a6e37f0e0afba7aef42048f15d90082ffc94b065b658a198ee99cddb263","abstract_canon_sha256":"5d0233b6de0eaf4d01fb90b0b9ec16c9916ddaf2dbfe984465621081959d60fa"},"schema_version":"1.0"},"canonical_sha256":"a3160ede086f06a73505f292596c2226fff52f5d4cc68ba9f3109b207384c60e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:19:24.872735Z","signature_b64":"puyFq8eHt/GYjhaBlTqo9cYWfaLkpFFMuF7Lmf3Ys3Nvt3OKY/+BewTf5kSWfOXSJYKG+UyjntIUZ4DNZum2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3160ede086f06a73505f292596c2226fff52f5d4cc68ba9f3109b207384c60e","last_reissued_at":"2026-07-05T10:19:24.872199Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:19:24.872199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.05994","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1arh0zl3NogEkhw628AKflxwPVFp9RTukPWCUGy88Z8JUeDzTMnG6Qv0PNydmxd4aFKvoWk7S1tHzk9HP5KoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:55:41.722001Z"},"content_sha256":"5233547b65a3b521e017d88159113c659c9e855707c117193730a3b4b0b76d9b","schema_version":"1.0","event_id":"sha256:5233547b65a3b521e017d88159113c659c9e855707c117193730a3b4b0b76d9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UMLA5XQIN4DKONIF6KJFS3BCE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Minhyun Kim","submitted_at":"2024-06-10T03:26:54Z","abstract_excerpt":"For nonlinear operators of fractional $p$-Laplace type, we consider two types of solutions to the nonlocal Dirichlet problem: Sobolev solutions based on fractional Sobolev spaces and Perron solutions based on superharmonic functions. These solutions give rise to two different concepts of regularity for boundary points, namely Sobolev and Perron regularity. We show that these two notions are equivalent and we also provide several characterizations of regular boundary points. Along the way, we give a new definition of Perron solutions, which is applicable to arbitrary exterior Dirichlet data $g:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05994","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.05994/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ezmnn1v/9eiroa1llA8H5plzVn6BAhaY1ig9ndIq4hxXFukjWOPJJkVkQQE3WkY/iZDVrBOLLDePdNRn4/wKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:55:41.722586Z"},"content_sha256":"2ead9617ab0fcdd9281126f586ba28b223275576a03e11c440000c7917c15bcd","schema_version":"1.0","event_id":"sha256:2ead9617ab0fcdd9281126f586ba28b223275576a03e11c440000c7917c15bcd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMLA5XQIN4DKONIF6KJFS3BCE3/bundle.json","state_url":"https://pith.science/pith/UMLA5XQIN4DKONIF6KJFS3BCE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMLA5XQIN4DKONIF6KJFS3BCE3/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":"2026-08-12T12:55:41Z","links":{"resolver":"https://pith.science/pith/UMLA5XQIN4DKONIF6KJFS3BCE3","bundle":"https://pith.science/pith/UMLA5XQIN4DKONIF6KJFS3BCE3/bundle.json","state":"https://pith.science/pith/UMLA5XQIN4DKONIF6KJFS3BCE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMLA5XQIN4DKONIF6KJFS3BCE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UMLA5XQIN4DKONIF6KJFS3BCE3","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":"5d0233b6de0eaf4d01fb90b0b9ec16c9916ddaf2dbfe984465621081959d60fa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-10T03:26:54Z","title_canon_sha256":"40480a6e37f0e0afba7aef42048f15d90082ffc94b065b658a198ee99cddb263"},"schema_version":"1.0","source":{"id":"2406.05994","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.05994","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"2406.05994v3","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.05994","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"UMLA5XQIN4DK","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"pith_short_16","alias_value":"UMLA5XQIN4DKONIF","created_at":"2026-07-05T10:19:24Z"},{"alias_kind":"pith_short_8","alias_value":"UMLA5XQI","created_at":"2026-07-05T10:19:24Z"}],"graph_snapshots":[{"event_id":"sha256:2ead9617ab0fcdd9281126f586ba28b223275576a03e11c440000c7917c15bcd","target":"graph","created_at":"2026-07-05T10:19:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.05994/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For nonlinear operators of fractional $p$-Laplace type, we consider two types of solutions to the nonlocal Dirichlet problem: Sobolev solutions based on fractional Sobolev spaces and Perron solutions based on superharmonic functions. These solutions give rise to two different concepts of regularity for boundary points, namely Sobolev and Perron regularity. We show that these two notions are equivalent and we also provide several characterizations of regular boundary points. Along the way, we give a new definition of Perron solutions, which is applicable to arbitrary exterior Dirichlet data $g:","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Minhyun Kim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-10T03:26:54Z","title":"Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05994","kind":"arxiv","version":3},"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":"sha256:5233547b65a3b521e017d88159113c659c9e855707c117193730a3b4b0b76d9b","target":"record","created_at":"2026-07-05T10:19:24Z","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":"5d0233b6de0eaf4d01fb90b0b9ec16c9916ddaf2dbfe984465621081959d60fa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-10T03:26:54Z","title_canon_sha256":"40480a6e37f0e0afba7aef42048f15d90082ffc94b065b658a198ee99cddb263"},"schema_version":"1.0","source":{"id":"2406.05994","kind":"arxiv","version":3}},"canonical_sha256":"a3160ede086f06a73505f292596c2226fff52f5d4cc68ba9f3109b207384c60e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3160ede086f06a73505f292596c2226fff52f5d4cc68ba9f3109b207384c60e","first_computed_at":"2026-07-05T10:19:24.872199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:19:24.872199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"puyFq8eHt/GYjhaBlTqo9cYWfaLkpFFMuF7Lmf3Ys3Nvt3OKY/+BewTf5kSWfOXSJYKG+UyjntIUZ4DNZum2CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:19:24.872735Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.05994","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5233547b65a3b521e017d88159113c659c9e855707c117193730a3b4b0b76d9b","sha256:2ead9617ab0fcdd9281126f586ba28b223275576a03e11c440000c7917c15bcd"],"state_sha256":"4b1d77ce4f4ed8bb01cc4629de7763db614ca898647c3169967efbbffcc2ccac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FqWJZhX0+egdmozR2Xj4YeWNxvPEcTVnh60ZZ6oZZsqPGA+UfKhpjCFeOgZv6uEaOordl2L+qvexYVhNMCjiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T12:55:41.728625Z","bundle_sha256":"33760a257edca1fda8935d01120f18b25751365b079f8138cae3ee2bc2277644"}}