{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GQVEKO4YALSRLH35ZR7RXMSRGI","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":"8027f810fce5597b33106d4404c6a1c3ee1232cc3276b44d699478481637fb06","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-08T09:25:51Z","title_canon_sha256":"4a393931498d3a8af2f24ea5e4d857c765defd63a3dce35ccbdf4dc366798c8a"},"schema_version":"1.0","source":{"id":"1301.1456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1456","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1456v1","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1456","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"GQVEKO4YALSR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GQVEKO4YALSRLH35","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GQVEKO4Y","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:bb1427f3874a42dcb40308e4873fd740998a1e97a4374184a56f911515bbebb5","target":"graph","created_at":"2026-05-18T03:36:57Z","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":"For a functional $\\E$ and a peak selection that picks up a global maximum of $\\E$ on varying cones, we study the convergence up to a subsequence to a critical point of the sequence generated by a mountain pass type algorithm. Moreover, by carefully choosing stepsizes, we establish the convergence of the whole sequence under a \"localization\" assumption on the critical point. We illustrate our results with two problems: an indefinite Schr\\\"odinger equation and a superlinear Schr\\\"odinger system.","authors_text":"Christopher Grumiau, Christophe Troestler","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-08T09:25:51Z","title":"Convergence of a mountain pass type algorithm for strongly indefinite problems and systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1456","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:e60a82447ce52508f3e0989a83ddc6b0faa2294618f0c67fe044a14f383b46d9","target":"record","created_at":"2026-05-18T03:36:57Z","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":"8027f810fce5597b33106d4404c6a1c3ee1232cc3276b44d699478481637fb06","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-08T09:25:51Z","title_canon_sha256":"4a393931498d3a8af2f24ea5e4d857c765defd63a3dce35ccbdf4dc366798c8a"},"schema_version":"1.0","source":{"id":"1301.1456","kind":"arxiv","version":1}},"canonical_sha256":"342a453b9802e5159f7dcc7f1bb251323f7c656a00893d50d216b67587393489","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"342a453b9802e5159f7dcc7f1bb251323f7c656a00893d50d216b67587393489","first_computed_at":"2026-05-18T03:36:57.464304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:57.464304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYmOCL9qIjH5qm6TI7RyQBbSptvy7Q++AwQqMVLsK+u3+37/BcCr3+MD00jRrbuktQPLkdkGJVUJGSq5oNyWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:57.465138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e60a82447ce52508f3e0989a83ddc6b0faa2294618f0c67fe044a14f383b46d9","sha256:bb1427f3874a42dcb40308e4873fd740998a1e97a4374184a56f911515bbebb5"],"state_sha256":"d4a51185a1c327bf16f2b444f5ceba89a58dbe948ae8790a162d02a51657faf4"}