{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:DIRXTVOZT5RQ3C5TN4C3LQEVPI","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":"8e18b4e63179210a2801588b2313ced49c9957f2a53e7016ac3c79994dfc468c","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2001-04-02T21:42:22Z","title_canon_sha256":"e44a7f449f5450676876135428bd6ad022c7ab91c721f1f146855e2256609448"},"schema_version":"1.0","source":{"id":"nlin/0104004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0104004","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0104004v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0104004","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"DIRXTVOZT5RQ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"DIRXTVOZT5RQ3C5T","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"DIRXTVOZ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:6334b2433879d6ba31dec9f1bc329372fb15859b15b165ea16368b07e2b4589a","target":"graph","created_at":"2026-05-18T01:05:22Z","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 study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves integrability via the inverse scattering transform (IST) method.\n  This IST-integrable class of equations contains both the KdV equation and the CH equation as limiting cases. It arises as the compatibility condition for a second order isospectral eigenvalue problem and a first order equation for the evolution of its eigenfunctions. This integrable equation is","authors_text":"Darryl D. Holm, Georg Gottwald, Holger R. Dullin","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2001-04-02T21:42:22Z","title":"An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0104004","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:a5124125aacc5e81f2160d489c7d3eda5335816ef8f93a74424e03c94f1f0d9e","target":"record","created_at":"2026-05-18T01:05:22Z","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":"8e18b4e63179210a2801588b2313ced49c9957f2a53e7016ac3c79994dfc468c","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2001-04-02T21:42:22Z","title_canon_sha256":"e44a7f449f5450676876135428bd6ad022c7ab91c721f1f146855e2256609448"},"schema_version":"1.0","source":{"id":"nlin/0104004","kind":"arxiv","version":1}},"canonical_sha256":"1a2379d5d99f630d8bb36f05b5c0957a0de1345c871c2bf00dbf5123a05c99d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a2379d5d99f630d8bb36f05b5c0957a0de1345c871c2bf00dbf5123a05c99d7","first_computed_at":"2026-05-18T01:05:22.209337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.209337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8G7ymVaOThdZAZDLAAPlLHYiYmuuyhvwgqF5hcjeB+x95xzpQxM4dcc3AYzaOWJOa4HokjtyLf7DQ/CUKRqQBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.209951Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0104004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5124125aacc5e81f2160d489c7d3eda5335816ef8f93a74424e03c94f1f0d9e","sha256:6334b2433879d6ba31dec9f1bc329372fb15859b15b165ea16368b07e2b4589a"],"state_sha256":"d6cffaa94b9b5f3777775b5ced6c1e94ff65a722b6988cb0aaf38d28325fc835"}