{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SHUCQ5AFLPZUXH46KYEZYSSNHX","short_pith_number":"pith:SHUCQ5AF","schema_version":"1.0","canonical_sha256":"91e82874055bf34b9f9e56099c4a4d3dd8307dccec7d5be2bbc8d0ff3052ed6a","source":{"kind":"arxiv","id":"1601.04184","version":1},"attestation_state":"computed","paper":{"title":"The Wiener Test for the Removability of the Logarithmic Singularity for the Elliptic PDEs with Measurable Coefficients and Its Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ugur G. Abdulla","submitted_at":"2016-01-16T17:26:00Z","abstract_excerpt":"This paper introduces the notion of $log$-regularity (or $log$-irregularity) of the boundary point $\\zeta$ (possibly $\\zeta=\\infty$) of the arbitrary open subset $\\Omega$ of the Greenian deleted neigborhood of $\\zeta$ in $R^2$ concerning second order uniformly elliptic equations with bounded and measurable coefficients, according as whether the $log$-harmonic measure of $\\zeta$ is null (or positive). A necessary and sufficient condition for the removability of the logarithmic singularity, that is to say for the existence of a unique solution to the Dirichlet problem in $\\Omega$ in a class $O(\\"},"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":"1601.04184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-16T17:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"d31e0ab484e7a6a20206a9ee1b0a649be4caf4150fb315c2d85357f41951d4c8","abstract_canon_sha256":"63a2e55830469be444407b276a991ddc35e9ef2c02fadb09d6a06136bc04be1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:32.806302Z","signature_b64":"HuVqVlbIiRTlcAwUguHYZhzyuQmGVhlkbHIYIiMhpJ8+J4oLJ2DVfxYFj1tVHQEsXWoKaF3pTg3FsKSo8GYoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91e82874055bf34b9f9e56099c4a4d3dd8307dccec7d5be2bbc8d0ff3052ed6a","last_reissued_at":"2026-05-18T00:04:32.805718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:32.805718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Wiener Test for the Removability of the Logarithmic Singularity for the Elliptic PDEs with Measurable Coefficients and Its Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ugur G. Abdulla","submitted_at":"2016-01-16T17:26:00Z","abstract_excerpt":"This paper introduces the notion of $log$-regularity (or $log$-irregularity) of the boundary point $\\zeta$ (possibly $\\zeta=\\infty$) of the arbitrary open subset $\\Omega$ of the Greenian deleted neigborhood of $\\zeta$ in $R^2$ concerning second order uniformly elliptic equations with bounded and measurable coefficients, according as whether the $log$-harmonic measure of $\\zeta$ is null (or positive). A necessary and sufficient condition for the removability of the logarithmic singularity, that is to say for the existence of a unique solution to the Dirichlet problem in $\\Omega$ in a class $O(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04184","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":"1601.04184","created_at":"2026-05-18T00:04:32.805784+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.04184v1","created_at":"2026-05-18T00:04:32.805784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04184","created_at":"2026-05-18T00:04:32.805784+00:00"},{"alias_kind":"pith_short_12","alias_value":"SHUCQ5AFLPZU","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SHUCQ5AFLPZUXH46","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SHUCQ5AF","created_at":"2026-05-18T12:30:44.179134+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/SHUCQ5AFLPZUXH46KYEZYSSNHX","json":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX.json","graph_json":"https://pith.science/api/pith-number/SHUCQ5AFLPZUXH46KYEZYSSNHX/graph.json","events_json":"https://pith.science/api/pith-number/SHUCQ5AFLPZUXH46KYEZYSSNHX/events.json","paper":"https://pith.science/paper/SHUCQ5AF"},"agent_actions":{"view_html":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX","download_json":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX.json","view_paper":"https://pith.science/paper/SHUCQ5AF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.04184&json=true","fetch_graph":"https://pith.science/api/pith-number/SHUCQ5AFLPZUXH46KYEZYSSNHX/graph.json","fetch_events":"https://pith.science/api/pith-number/SHUCQ5AFLPZUXH46KYEZYSSNHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX/action/storage_attestation","attest_author":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX/action/author_attestation","sign_citation":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX/action/citation_signature","submit_replication":"https://pith.science/pith/SHUCQ5AFLPZUXH46KYEZYSSNHX/action/replication_record"}},"created_at":"2026-05-18T00:04:32.805784+00:00","updated_at":"2026-05-18T00:04:32.805784+00:00"}