{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QZXK2BEQROXAM4734K36K72IZS","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":"c7ea44d45fd64f80ff9b2131492307e254b82d134b30f587f1d2b2a2085739a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T10:37:03Z","title_canon_sha256":"8927cfecd7c5fffcd8c3c964990e85ac84115b74a5efbf6c2cc534443831101b"},"schema_version":"1.0","source":{"id":"1811.08168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08168","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08168v1","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08168","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"QZXK2BEQROXA","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QZXK2BEQROXAM473","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QZXK2BEQ","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:c99c36cf0633e4256330d3c33ae37e083f8807e0947d5a6b01a030f7278fd5e4","target":"graph","created_at":"2026-05-18T00:00:16Z","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 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.","authors_text":"Rainer Mandel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T10:37:03Z","title":"Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08168","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":"sha256:05e226d50cb6183c284962c7a8698c4f1dbb3cae2fb07d26be21d133612348ed","target":"record","created_at":"2026-05-18T00:00:16Z","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":"c7ea44d45fd64f80ff9b2131492307e254b82d134b30f587f1d2b2a2085739a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T10:37:03Z","title_canon_sha256":"8927cfecd7c5fffcd8c3c964990e85ac84115b74a5efbf6c2cc534443831101b"},"schema_version":"1.0","source":{"id":"1811.08168","kind":"arxiv","version":1}},"canonical_sha256":"866ead04908bae0673fbe2b7e57f48cc8d561b38b99a57093c9d53a73c51b5d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"866ead04908bae0673fbe2b7e57f48cc8d561b38b99a57093c9d53a73c51b5d0","first_computed_at":"2026-05-18T00:00:16.640063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:16.640063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTk8mettITVzXcEeqW94S1x6FGQHZYXEHrs4HB+EsAeqclbRrGLgewrywD/RT9kJni8LJFMAKHU7DQ5eK1vyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:16.640831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05e226d50cb6183c284962c7a8698c4f1dbb3cae2fb07d26be21d133612348ed","sha256:c99c36cf0633e4256330d3c33ae37e083f8807e0947d5a6b01a030f7278fd5e4"],"state_sha256":"779ffcd92125f12b382d92fa77e2d5ff57777336b9a5521dceb2cf886a74b933"}