{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CWLSOYM6B4DIE66WI3K2AFSR7L","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":"6be1f8bf787dbeadd3c841194e0ac3773d51a0f37f4828060d9aebfab418c864","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-08T01:13:35Z","title_canon_sha256":"5388b9484fb3383e234d40c88b7e65e4caa20cb0d10ece968ba125a645e3b51e"},"schema_version":"1.0","source":{"id":"1212.1748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1748","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1748v1","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1748","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"CWLSOYM6B4DI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CWLSOYM6B4DIE66W","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CWLSOYM6","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:3b052bc878753f2b75bb6a1456b50c2c96a45f66c821dbba1095d0cb25882517","target":"graph","created_at":"2026-05-18T03:38:55Z","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 inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS) equations, Kadomtzev-Petviashvili and many more completely integrable PDEs of mathematical physics are solved, using Zacharv-Shabath scheme. This last approach includes the use of a Lax pair, and has an advantage to be applied to wider class of equations, like difference equations, but has a disadvantage to be used only for \"rapidly decreasing solutions\". This t","authors_text":"Andrey Melnikov","cross_cats":["math-ph","math.FA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-08T01:13:35Z","title":"A new method for solving completely integrable PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1748","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":"sha256:0bc22833247ffd423a471a358c7f3fb9a3376dc1d9f2d764fe76a88dd4fe732d","target":"record","created_at":"2026-05-18T03:38:55Z","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":"6be1f8bf787dbeadd3c841194e0ac3773d51a0f37f4828060d9aebfab418c864","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-08T01:13:35Z","title_canon_sha256":"5388b9484fb3383e234d40c88b7e65e4caa20cb0d10ece968ba125a645e3b51e"},"schema_version":"1.0","source":{"id":"1212.1748","kind":"arxiv","version":1}},"canonical_sha256":"159727619e0f06827bd646d5a01651fac3c8742e01e7663e84268eb042cece64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"159727619e0f06827bd646d5a01651fac3c8742e01e7663e84268eb042cece64","first_computed_at":"2026-05-18T03:38:55.236955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:55.236955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/Px9M4eFQlNRo7SMTJ0PmvezOuq/raqtxR3j0JeeTKAzi9kuIO4xLzdMHAyFHhhnz/WG80c5H71NeSiiu1WDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:55.237496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bc22833247ffd423a471a358c7f3fb9a3376dc1d9f2d764fe76a88dd4fe732d","sha256:3b052bc878753f2b75bb6a1456b50c2c96a45f66c821dbba1095d0cb25882517"],"state_sha256":"6beb48ff68cd4ef86111925a4856779942611e6289a3f689535445ceaebea576"}