{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TLU55V2YW6ACHHVT5RZKWSLR4Q","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":"2cb36d3219890c81db6156991025f1443cd7cf59fd22103f9475f79582c8a957","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T17:59:38Z","title_canon_sha256":"d90dd9e4c81be155b2a46cdde0f11add1822d8a382de363c3f4c8251f812f32e"},"schema_version":"1.0","source":{"id":"1302.0233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0233","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0233v1","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0233","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"TLU55V2YW6AC","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TLU55V2YW6ACHHVT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TLU55V2Y","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:4a99c49b3f61dbdfb11958768d337de25fe8debe467f2f38e198503345e94d46","target":"graph","created_at":"2026-05-18T02:31:02Z","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 various boundary and inner regularity questions for $p(\\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\\cdot)$-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded $p(\\cdot)$-harmonic functions and give some new characterizations of $W^{1, p(\\cdot)}_0$ spac","authors_text":"Anders Bj\\\"orn, Jana Bj\\\"orn, Tomasz Adamowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T17:59:38Z","title":"Regularity of $p(\\cdot)$-superharmonic functions, the Kellogg property and semiregular boundary points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0233","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":"sha256:02711109408a5f2bcaf655380cf08a14d8aab1f982c6a0bb85b53e6d398a68f0","target":"record","created_at":"2026-05-18T02:31:02Z","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":"2cb36d3219890c81db6156991025f1443cd7cf59fd22103f9475f79582c8a957","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T17:59:38Z","title_canon_sha256":"d90dd9e4c81be155b2a46cdde0f11add1822d8a382de363c3f4c8251f812f32e"},"schema_version":"1.0","source":{"id":"1302.0233","kind":"arxiv","version":1}},"canonical_sha256":"9ae9ded758b780239eb3ec72ab4971e41dad1f48e3ff9071725b52415d7b11b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ae9ded758b780239eb3ec72ab4971e41dad1f48e3ff9071725b52415d7b11b1","first_computed_at":"2026-05-18T02:31:02.532539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:02.532539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/iVRrBmrzNQUJo685cYZS02a4ditQO09eRieMa8lHnVs6BjCuPPvVa2AaWBRJvUVNf3gw9RWRkX2UJ21gVODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:02.532996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02711109408a5f2bcaf655380cf08a14d8aab1f982c6a0bb85b53e6d398a68f0","sha256:4a99c49b3f61dbdfb11958768d337de25fe8debe467f2f38e198503345e94d46"],"state_sha256":"1d0287df70543e63edcb36ac768164fdfe5a0aa751c1db4f66baf8cee4499e47"}