{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:223GTZPFZDA7IX3AI556KJL4RH","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":"4f07f690fac5b19c786f9b0154575b093bf9747dd0a508d3621200e667026831","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-04-26T19:09:44Z","title_canon_sha256":"125fdae82a747d21b80c170362763cedb58a63f300fd46722470cedc79f24c3b"},"schema_version":"1.0","source":{"id":"1004.4607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4607","created_at":"2026-05-18T02:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4607v1","created_at":"2026-05-18T02:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4607","created_at":"2026-05-18T02:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"223GTZPFZDA7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"223GTZPFZDA7IX3A","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"223GTZPF","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:90ac9d4d6d3dc199a758f3031501a1d3ca8023891f71c839cc4e4b794fc40cc5","target":"graph","created_at":"2026-05-18T02:07:53Z","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":"The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the  Kadomtsev-Petviashvili (KP) equation.  The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. Each soliton solution is then defined by a point of the totally non-negative Grassmann variety which can be parametrized  by a unique derangement of the symmetric group of permutations. Our study also includes certain numerical  stability problems of those soliton solutions. Numerical simulations of the initial value problems  indica","authors_text":"Yuji Kodama","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-04-26T19:09:44Z","title":"KP solitons in shallow water"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4607","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":"sha256:08cd77c6979008e8a92411d6bcfeb8bfd1efbf48db279d5670632d73b8eabf29","target":"record","created_at":"2026-05-18T02:07:53Z","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":"4f07f690fac5b19c786f9b0154575b093bf9747dd0a508d3621200e667026831","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2010-04-26T19:09:44Z","title_canon_sha256":"125fdae82a747d21b80c170362763cedb58a63f300fd46722470cedc79f24c3b"},"schema_version":"1.0","source":{"id":"1004.4607","kind":"arxiv","version":1}},"canonical_sha256":"d6b669e5e5c8c1f45f60477be5257c89c4d77f66aa51ec24a54f9efe8c8165c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6b669e5e5c8c1f45f60477be5257c89c4d77f66aa51ec24a54f9efe8c8165c4","first_computed_at":"2026-05-18T02:07:53.720170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:53.720170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZeXQbuu8Q/dtkFNbpZONawBOHi9fok2uQ6UvX9ev5Q0F4Llplin27YY7KVF+kBpc+wx6gmd/3X2fnqEztHYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:53.720804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08cd77c6979008e8a92411d6bcfeb8bfd1efbf48db279d5670632d73b8eabf29","sha256:90ac9d4d6d3dc199a758f3031501a1d3ca8023891f71c839cc4e4b794fc40cc5"],"state_sha256":"32718fe51a0768188a07436f67a0ab9303136ddd35617b785afff80a1e5ef9ac"}