{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:WPCSD2YKUZCSL5ENJ5XHDH5GUJ","short_pith_number":"pith:WPCSD2YK","schema_version":"1.0","canonical_sha256":"b3c521eb0aa64525f48d4f6e719fa6a245fc97188af14cad86854ddd39733eba","source":{"kind":"arxiv","id":"1101.0418","version":1},"attestation_state":"computed","paper":{"title":"Removable Sets for H\\\"older Continuous p(x)-Harmonic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Lyaghfouri","submitted_at":"2011-01-02T17:32:40Z","abstract_excerpt":"We establish that a closed set $E$ is removable for $C^{0,\\alpha}$ H\\\"{o}lder continuous $p(x)$-harmonic functions in a bounded open domain $\\Omega$ of $\\mathbb{R}^n$, $n\\geq 2$, provided that for each compact subset $K$ of $E$, the $(n-p_K+\\alpha(p_K-1))$-Hausdorff measure of $K$ is zero, where $p_K=\\max_{x\\in K} p(x)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.0418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-02T17:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"ec0061cafbd46b847a66e389154e1a198d89cf316ab49f0c75040dd3dd74cc7b","abstract_canon_sha256":"2d7dc30dee790f1831171749f8935ce2dc9ccc5fad8af0447c4a1bae7bae144d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:10.402413Z","signature_b64":"iIHWQyBZ+ZKpBGAoCY5Q1g6wwwRG+ScQyD/0Hwyi/Q+ylMZWwvdeGlvdSvyGvoFkFqkO6DCaQwx5C00Z6sq1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c521eb0aa64525f48d4f6e719fa6a245fc97188af14cad86854ddd39733eba","last_reissued_at":"2026-05-18T04:32:10.401904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:10.401904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Removable Sets for H\\\"older Continuous p(x)-Harmonic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Lyaghfouri","submitted_at":"2011-01-02T17:32:40Z","abstract_excerpt":"We establish that a closed set $E$ is removable for $C^{0,\\alpha}$ H\\\"{o}lder continuous $p(x)$-harmonic functions in a bounded open domain $\\Omega$ of $\\mathbb{R}^n$, $n\\geq 2$, provided that for each compact subset $K$ of $E$, the $(n-p_K+\\alpha(p_K-1))$-Hausdorff measure of $K$ is zero, where $p_K=\\max_{x\\in K} p(x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0418","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.0418","created_at":"2026-05-18T04:32:10.401987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.0418v1","created_at":"2026-05-18T04:32:10.401987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0418","created_at":"2026-05-18T04:32:10.401987+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPCSD2YKUZCS","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPCSD2YKUZCSL5EN","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPCSD2YK","created_at":"2026-05-18T12:26:44.992195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ","json":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ.json","graph_json":"https://pith.science/api/pith-number/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/graph.json","events_json":"https://pith.science/api/pith-number/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/events.json","paper":"https://pith.science/paper/WPCSD2YK"},"agent_actions":{"view_html":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ","download_json":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ.json","view_paper":"https://pith.science/paper/WPCSD2YK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.0418&json=true","fetch_graph":"https://pith.science/api/pith-number/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/graph.json","fetch_events":"https://pith.science/api/pith-number/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/action/storage_attestation","attest_author":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/action/author_attestation","sign_citation":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/action/citation_signature","submit_replication":"https://pith.science/pith/WPCSD2YKUZCSL5ENJ5XHDH5GUJ/action/replication_record"}},"created_at":"2026-05-18T04:32:10.401987+00:00","updated_at":"2026-05-18T04:32:10.401987+00:00"}