{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TIXVTKUPF7YKXOJ55DQK2SI7JS","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":"c9da37cb3a056e3a6fd528463883bd53bd252b94a3b451e985da282b491d2ad1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-10T15:59:22Z","title_canon_sha256":"02820de8dd53a21d1f1e35ac332663de62cc0d1a2ed7460f50285aa8bdf9a32e"},"schema_version":"1.0","source":{"id":"0912.2027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2027","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2027v2","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2027","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"TIXVTKUPF7YK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TIXVTKUPF7YKXOJ5","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TIXVTKUP","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:114b70456cfdeec87d022285780d90f0415b5da94b184214539272b3b9947494","target":"graph","created_at":"2026-05-18T04:03:07Z","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 consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\\\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and long waves. Using the compensated compactness method, we prove convergence of approximate solutions generated by semi-discrete finite volume type methods towards the unique entropy solution of the Cauchy problem. Some numerical examples are presented.","authors_text":"M\\'ario Figueira, Paulo Amorim","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-10T15:59:22Z","title":"Convergence of numerical schemes for short wave long wave interaction equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2027","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:b117299f240c7c1e50daaedd9683e31f8c6f954f889cf3054938091716f062b9","target":"record","created_at":"2026-05-18T04:03:07Z","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":"c9da37cb3a056e3a6fd528463883bd53bd252b94a3b451e985da282b491d2ad1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-10T15:59:22Z","title_canon_sha256":"02820de8dd53a21d1f1e35ac332663de62cc0d1a2ed7460f50285aa8bdf9a32e"},"schema_version":"1.0","source":{"id":"0912.2027","kind":"arxiv","version":2}},"canonical_sha256":"9a2f59aa8f2ff0abb93de8e0ad491f4caf47d9b7d04af0e4330569de7ee439d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a2f59aa8f2ff0abb93de8e0ad491f4caf47d9b7d04af0e4330569de7ee439d6","first_computed_at":"2026-05-18T04:03:07.556745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:07.556745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lw24opBjXfds9CmOKcYpqOn71RoP71nsdM+VvWQYqrm+XLLelR6tMFJNHQo0IYsdCtBecv3oBcRwtwxOnTh+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:07.557513Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b117299f240c7c1e50daaedd9683e31f8c6f954f889cf3054938091716f062b9","sha256:114b70456cfdeec87d022285780d90f0415b5da94b184214539272b3b9947494"],"state_sha256":"90d38b4ed8b05b7abb22c5485cdea47421395205f0a7634a0f33bff4e1a1fce2"}