{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DGH3ANEB2KDQFBWO2AAVUT4L2Z","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":"dcb6e67a2acc8e113b77228a74e7ddd3d4726d259f7b1b37ea6f98fb612c0fa5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-06T14:51:22Z","title_canon_sha256":"c780511fca51d489592246f5eb3c82bff38ff7614b57ad5ce23f1b93b7fb8338"},"schema_version":"1.0","source":{"id":"1407.1503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1503","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1503v1","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1503","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"pith_short_12","alias_value":"DGH3ANEB2KDQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DGH3ANEB2KDQFBWO","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DGH3ANEB","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8896c14a1b4f11f1e742963fbee24cb2c1505b072b2879cc741329bf5c22416b","target":"graph","created_at":"2026-05-18T02:48:16Z","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":"In this article we classify vessels producing solutions of some completely integrable PDEs, presenting a \\textit{unified} approach for them. The classification includes such important examples as Korteweg-de Vries (KdV) and evolutionary Non Linear Schr\\\" odingier (ENLS) equations. In fact, employing basic matrix algebra techniques it is shown that there are exactly two canonical forms of such vessels, so that each canonical form generalize either KdV or ENLS equations. Particularly, Dirac canonical systems, whose evolution was recently inserted into the vessel theory, are shown to be equivalen","authors_text":"Andrey Melnikov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-06T14:51:22Z","title":"Classification of KdV vessels with constant parameters and two dimensional outer space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1503","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:df85a887dba677e589b8c385f048a4544873f6b44ddaf52eb6d4f881c6342d3b","target":"record","created_at":"2026-05-18T02:48:16Z","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":"dcb6e67a2acc8e113b77228a74e7ddd3d4726d259f7b1b37ea6f98fb612c0fa5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-06T14:51:22Z","title_canon_sha256":"c780511fca51d489592246f5eb3c82bff38ff7614b57ad5ce23f1b93b7fb8338"},"schema_version":"1.0","source":{"id":"1407.1503","kind":"arxiv","version":1}},"canonical_sha256":"198fb03481d2870286ced0015a4f8bd65eb65880c0b9d1b24e4c5c288d528049","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"198fb03481d2870286ced0015a4f8bd65eb65880c0b9d1b24e4c5c288d528049","first_computed_at":"2026-05-18T02:48:16.388619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:16.388619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VenP+ozE9UgkiD7J1BWs3Qe5sRdigDOHpboM04r38jVbpmPVdJIb1xjkJN7GgAVuSOErlo18glLQkrUEjsatCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:16.389253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df85a887dba677e589b8c385f048a4544873f6b44ddaf52eb6d4f881c6342d3b","sha256:8896c14a1b4f11f1e742963fbee24cb2c1505b072b2879cc741329bf5c22416b"],"state_sha256":"ba77abfa67a3b2fdc3a2b1d27c513a97e0a4937f8a642604e9cb4057c8630ebd"}