{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RJA5A7KO6HRAIJUBANVXHPLNXW","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":"b79bfef0de6d5650bd4a6482ef5d2f4913d7701e8024b2ddb1552dac17bc90fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T15:03:28Z","title_canon_sha256":"cff5b1f813d183abc52ef31b2e273e51b314e02bda021b5a1ed92c7287988b78"},"schema_version":"1.0","source":{"id":"1710.06332","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06332","created_at":"2026-05-18T00:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06332v2","created_at":"2026-05-18T00:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06332","created_at":"2026-05-18T00:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"RJA5A7KO6HRA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RJA5A7KO6HRAIJUB","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RJA5A7KO","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:86c1494dfa58c9f738d09a9c82abb77476089a5a60f2fc76cbeea391f3180bf5","target":"graph","created_at":"2026-05-18T00:17:42Z","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 prove an $L^p$-version of the limiting absoprtion principle for a class of periodic elliptic differential operators of second order. The result is applied to the construction of nontrivial solutions of nonlinear Helmholtz equations with periodic coefficient functions.","authors_text":"Rainer Mandel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T15:03:28Z","title":"The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06332","kind":"arxiv","version":2},"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":"sha256:2c887e512b7fe54fd8215b00a7d133d1017428182cb2b5695472abc15c5d0a5c","target":"record","created_at":"2026-05-18T00:17:42Z","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":"b79bfef0de6d5650bd4a6482ef5d2f4913d7701e8024b2ddb1552dac17bc90fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T15:03:28Z","title_canon_sha256":"cff5b1f813d183abc52ef31b2e273e51b314e02bda021b5a1ed92c7287988b78"},"schema_version":"1.0","source":{"id":"1710.06332","kind":"arxiv","version":2}},"canonical_sha256":"8a41d07d4ef1e2042681036b73bd6dbda390e48201a35758b833fd8072109d83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a41d07d4ef1e2042681036b73bd6dbda390e48201a35758b833fd8072109d83","first_computed_at":"2026-05-18T00:17:42.666717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:42.666717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+LBFk7+iVPyxUWzkTijsBbvrp5Zapmbcafdt4mvFCpMvLMeLhFqPBUL31j0aA8obVLUWJlG++/l5DeWTog3lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:42.667444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06332","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c887e512b7fe54fd8215b00a7d133d1017428182cb2b5695472abc15c5d0a5c","sha256:86c1494dfa58c9f738d09a9c82abb77476089a5a60f2fc76cbeea391f3180bf5"],"state_sha256":"205189be63206415d80584e2247f1c239279f777c67a1a17e195b551370f0a19"}