{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4JURSYAJFBBYZIA223HAQWBL7K","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":"0300ef24fcb2a6b43796cd75196c110f6b7050a32cab58ec8f4785c5ee128fe1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T08:17:16Z","title_canon_sha256":"58254bf9334f64d5362b72a454537025e07a53f331db470c448aefa08e8a497d"},"schema_version":"1.0","source":{"id":"1604.06281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06281","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06281v1","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06281","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"4JURSYAJFBBY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4JURSYAJFBBYZIA2","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4JURSYAJ","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b253cdaf8d5ea0093da92b70ec869dd79f7aa1c9b613937bbd8ccb3e16a529e7","target":"graph","created_at":"2026-05-18T01:16:32Z","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":"A system of equations consisting of an infinite string coupled to a nonlinear oscillator is considered. The Cauchy problem for the system with the periodic initial data is studied. The main goal is to prove the convergence of the solutions as $t\\to\\infty$ to a time periodic solution.","authors_text":"T.V. Dudnikova","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T08:17:16Z","title":"Boundedness and convergence of solutions for the string coupled to a nonlinear oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06281","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:f0fb4c4bf2fdae4c89426b9506a562c1ade0eda094ef5a771d25252508491d36","target":"record","created_at":"2026-05-18T01:16:32Z","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":"0300ef24fcb2a6b43796cd75196c110f6b7050a32cab58ec8f4785c5ee128fe1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-20T08:17:16Z","title_canon_sha256":"58254bf9334f64d5362b72a454537025e07a53f331db470c448aefa08e8a497d"},"schema_version":"1.0","source":{"id":"1604.06281","kind":"arxiv","version":1}},"canonical_sha256":"e26919600928438ca01ad6ce08582bfab3b5fda3201df8933db2cb73d2b901ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e26919600928438ca01ad6ce08582bfab3b5fda3201df8933db2cb73d2b901ae","first_computed_at":"2026-05-18T01:16:32.112636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:32.112636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xDUh9LqAOwEePvt0ibO/lP37xKBy/A6E9b3tHPyEpav75n/3v7NlUWcm3ujtmfGWgdM+tg31MstyLpYjBlqxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:32.113285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0fb4c4bf2fdae4c89426b9506a562c1ade0eda094ef5a771d25252508491d36","sha256:b253cdaf8d5ea0093da92b70ec869dd79f7aa1c9b613937bbd8ccb3e16a529e7"],"state_sha256":"0253a0f22b3755ee4d7fcdb38a4e6075b9d6f25b8ff3aff693ebdb4aa121f1fb"}