{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BRXWJW5HXPH75YRBSAAEWSHATS","short_pith_number":"pith:BRXWJW5H","schema_version":"1.0","canonical_sha256":"0c6f64dba7bbcffee22190004b48e09c9184e78ad406a6a05231212df488ef4c","source":{"kind":"arxiv","id":"1104.4237","version":4},"attestation_state":"computed","paper":{"title":"Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miren Zubeldia","submitted_at":"2011-04-21T11:39:01Z","abstract_excerpt":"We study the following Helmholtz equation $$ (\\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + \\lambda u = f(x) $$ in $\\mathbb{R}^d$ with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type."},"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":"1104.4237","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-21T11:39:01Z","cross_cats_sorted":[],"title_canon_sha256":"2dfd5c0866f4f8773e44b17fb382b1773e84f2e62f3904f9c2ddaab8ac5a7357","abstract_canon_sha256":"1ff24a1d567d6b35695d1e8e0768b405a73205b35dfc3943e1e7dd24e886c427"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:43.809847Z","signature_b64":"xutiAy1J15ROr+c8vOfHKrAOn1fOxQabX04f0s3VeQPgVDjcGfxfOvy85/C5ak4JtP6QKglZnJ5XvTJV9nnRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c6f64dba7bbcffee22190004b48e09c9184e78ad406a6a05231212df488ef4c","last_reissued_at":"2026-05-18T03:13:43.809205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:43.809205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miren Zubeldia","submitted_at":"2011-04-21T11:39:01Z","abstract_excerpt":"We study the following Helmholtz equation $$ (\\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + \\lambda u = f(x) $$ in $\\mathbb{R}^d$ with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4237","kind":"arxiv","version":4},"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":"1104.4237","created_at":"2026-05-18T03:13:43.809289+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.4237v4","created_at":"2026-05-18T03:13:43.809289+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4237","created_at":"2026-05-18T03:13:43.809289+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRXWJW5HXPH7","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRXWJW5HXPH75YRB","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRXWJW5H","created_at":"2026-05-18T12:26:24.575870+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/BRXWJW5HXPH75YRBSAAEWSHATS","json":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS.json","graph_json":"https://pith.science/api/pith-number/BRXWJW5HXPH75YRBSAAEWSHATS/graph.json","events_json":"https://pith.science/api/pith-number/BRXWJW5HXPH75YRBSAAEWSHATS/events.json","paper":"https://pith.science/paper/BRXWJW5H"},"agent_actions":{"view_html":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS","download_json":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS.json","view_paper":"https://pith.science/paper/BRXWJW5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.4237&json=true","fetch_graph":"https://pith.science/api/pith-number/BRXWJW5HXPH75YRBSAAEWSHATS/graph.json","fetch_events":"https://pith.science/api/pith-number/BRXWJW5HXPH75YRBSAAEWSHATS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS/action/storage_attestation","attest_author":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS/action/author_attestation","sign_citation":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS/action/citation_signature","submit_replication":"https://pith.science/pith/BRXWJW5HXPH75YRBSAAEWSHATS/action/replication_record"}},"created_at":"2026-05-18T03:13:43.809289+00:00","updated_at":"2026-05-18T03:13:43.809289+00:00"}