{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZLHKA2DHLQEDUIHITIZC5CQBI5","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":"e467743b6437699c4c6a59c42a883d4d8b0f6b07b28173468324f597ad5ddd45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-24T20:21:12Z","title_canon_sha256":"c0e7100c3baf2373c9ca60168c299833372353e95a0a57f61308647e7bc1da30"},"schema_version":"1.0","source":{"id":"1411.6599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6599","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6599v2","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6599","created_at":"2026-05-18T01:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZLHKA2DHLQED","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZLHKA2DHLQEDUIHI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZLHKA2DH","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:66165fe9db7fe18c126bbc3d2102dee3f097ae4d44f250ac68a183742eecb0eb","target":"graph","created_at":"2026-05-18T01:36:48Z","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 investigate some well-posedness issues for the initial value problem (IVP) associated to the system \\begin{equation} \\{ \\begin{array} [c]{l} 2i\\partial_{t}u+q\\partial_{x}^{2}u+i\\gamma\\partial_{x}^{3}u=F_{1}(u,w)\\\\ 2i\\partial_{t}w+q\\partial_{x}^{2}w+i\\gamma\\partial_{x}^{3}w=F_{2}(u,w), \\end{array} . \\end{equation} where $F_{1}$ and $F_{2}$ are polynomials of degree 3 involving $u$, $w$ and their derivatives. This system describes the dynamics of two nonlinear short-optical pulses envelopes $u(x,t)$ and $w(x,t)$ in fibers (\\cite{31}, \\cite{14}). We prove periodic local well-posedness for the ","authors_text":"Luciana Bragan\\c{c}a, Marcia Scialom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-24T20:21:12Z","title":"On the Periodic Cauchy problem for a coupled system of third-order nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6599","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:cf6c8d102b11c1011e9b266f5fde27090e1687322366a2a71b8fb0c83c6d3e2d","target":"record","created_at":"2026-05-18T01:36:48Z","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":"e467743b6437699c4c6a59c42a883d4d8b0f6b07b28173468324f597ad5ddd45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-24T20:21:12Z","title_canon_sha256":"c0e7100c3baf2373c9ca60168c299833372353e95a0a57f61308647e7bc1da30"},"schema_version":"1.0","source":{"id":"1411.6599","kind":"arxiv","version":2}},"canonical_sha256":"cacea068675c083a20e89a322e8a01475d53b591fed49c32eb85b9fd263e401a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cacea068675c083a20e89a322e8a01475d53b591fed49c32eb85b9fd263e401a","first_computed_at":"2026-05-18T01:36:48.161844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:48.161844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D3WYDdjscPmaLBboax3cvu6sUIIWUoHhvmRKAvfs5ziO31uJX8CxHCyP/DB5IGdrtjC8SRUw3thpEpNAnIg4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:48.162546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf6c8d102b11c1011e9b266f5fde27090e1687322366a2a71b8fb0c83c6d3e2d","sha256:66165fe9db7fe18c126bbc3d2102dee3f097ae4d44f250ac68a183742eecb0eb"],"state_sha256":"6451e6a8337a33c3e5ea132dc353699ac4e9bbbe080837f30ac0370986887d7c"}