{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QZXK2BEQROXAM4734K36K72IZS","short_pith_number":"pith:QZXK2BEQ","schema_version":"1.0","canonical_sha256":"866ead04908bae0673fbe2b7e57f48cc8d561b38b99a57093c9d53a73c51b5d0","source":{"kind":"arxiv","id":"1811.08168","version":1},"attestation_state":"computed","paper":{"title":"Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2018-11-20T10:37:03Z","abstract_excerpt":"We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. As an auxiliary tool a Limiting Absorption Principle for the curl-curl operator is proved."},"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":"1811.08168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T10:37:03Z","cross_cats_sorted":[],"title_canon_sha256":"8927cfecd7c5fffcd8c3c964990e85ac84115b74a5efbf6c2cc534443831101b","abstract_canon_sha256":"c7ea44d45fd64f80ff9b2131492307e254b82d134b30f587f1d2b2a2085739a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:16.640831Z","signature_b64":"sTk8mettITVzXcEeqW94S1x6FGQHZYXEHrs4HB+EsAeqclbRrGLgewrywD/RT9kJni8LJFMAKHU7DQ5eK1vyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"866ead04908bae0673fbe2b7e57f48cc8d561b38b99a57093c9d53a73c51b5d0","last_reissued_at":"2026-05-18T00:00:16.640063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:16.640063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2018-11-20T10:37:03Z","abstract_excerpt":"We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. As an auxiliary tool a Limiting Absorption Principle for the curl-curl operator is proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08168","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":"1811.08168","created_at":"2026-05-18T00:00:16.640178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.08168v1","created_at":"2026-05-18T00:00:16.640178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08168","created_at":"2026-05-18T00:00:16.640178+00:00"},{"alias_kind":"pith_short_12","alias_value":"QZXK2BEQROXA","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"QZXK2BEQROXAM473","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"QZXK2BEQ","created_at":"2026-05-18T12:32:50.500415+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/QZXK2BEQROXAM4734K36K72IZS","json":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS.json","graph_json":"https://pith.science/api/pith-number/QZXK2BEQROXAM4734K36K72IZS/graph.json","events_json":"https://pith.science/api/pith-number/QZXK2BEQROXAM4734K36K72IZS/events.json","paper":"https://pith.science/paper/QZXK2BEQ"},"agent_actions":{"view_html":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS","download_json":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS.json","view_paper":"https://pith.science/paper/QZXK2BEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.08168&json=true","fetch_graph":"https://pith.science/api/pith-number/QZXK2BEQROXAM4734K36K72IZS/graph.json","fetch_events":"https://pith.science/api/pith-number/QZXK2BEQROXAM4734K36K72IZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS/action/storage_attestation","attest_author":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS/action/author_attestation","sign_citation":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS/action/citation_signature","submit_replication":"https://pith.science/pith/QZXK2BEQROXAM4734K36K72IZS/action/replication_record"}},"created_at":"2026-05-18T00:00:16.640178+00:00","updated_at":"2026-05-18T00:00:16.640178+00:00"}