{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PF3P5N6MPVIEFOCIWACEQMOTCZ","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":"530f52312d4fca0770e70699359862864e1b3de781a33200309dd8d2e1646052","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-13T13:44:04Z","title_canon_sha256":"e4a1dddc1940a5d35aab813cc70d868f29be3004188a3ae49db4ca69c19945db"},"schema_version":"1.0","source":{"id":"1605.04178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04178","created_at":"2026-05-18T01:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04178v1","created_at":"2026-05-18T01:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04178","created_at":"2026-05-18T01:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"PF3P5N6MPVIE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PF3P5N6MPVIEFOCI","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PF3P5N6M","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:56618a18cfe795560fa3d4ef18efab69935a9c3867ce67181c2c0ca9d8a7f6a6","target":"graph","created_at":"2026-05-18T01:14:54Z","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":"The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and no examples were ever given. We show that seemingly different classical result by Lazer and Leach [11], on forced harmonic oscillators at resonance, provides an example for this theorem. The article by Williams [14] also contained a shorter proof. We use a similar approach to study resonance for $2 \\times 2$ systems. We derive conditions for existence of so","authors_text":"Philip Korman","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-13T13:44:04Z","title":"Nonlinear elliptic equations and systems with linear part at resonance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04178","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:bc50057afa076333f86eb884ef5c27cf05123371cd865f3deba55c67a56528d5","target":"record","created_at":"2026-05-18T01:14:54Z","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":"530f52312d4fca0770e70699359862864e1b3de781a33200309dd8d2e1646052","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-13T13:44:04Z","title_canon_sha256":"e4a1dddc1940a5d35aab813cc70d868f29be3004188a3ae49db4ca69c19945db"},"schema_version":"1.0","source":{"id":"1605.04178","kind":"arxiv","version":1}},"canonical_sha256":"7976feb7cc7d5042b848b0044831d3165213297d1c64a1f9e82302efafbc8200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7976feb7cc7d5042b848b0044831d3165213297d1c64a1f9e82302efafbc8200","first_computed_at":"2026-05-18T01:14:54.099753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:54.099753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+t2f0EvX+3AgTAMiL7HwhRuCm98TFjnRwxkbRLYg3DbeSVYmBh9/1UKaGMFD1/4rEvjmhgMqJrFX0XtVoV+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:54.100179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc50057afa076333f86eb884ef5c27cf05123371cd865f3deba55c67a56528d5","sha256:56618a18cfe795560fa3d4ef18efab69935a9c3867ce67181c2c0ca9d8a7f6a6"],"state_sha256":"ade3d3570614028a202a4950fb6c460028d7d481ef325359991c5dd93ab3e370"}