{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AVAMH6JMV2QNOKO4ZNZ2RGGTXZ","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":"23e37f621fcfd3c3f5cf1d02445f8da40785920ef0522e5bc990edaadec47647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-01-03T20:59:22Z","title_canon_sha256":"7f9c5619aa6fd480013c346f22c8202eec11d8f7f57cecfde81ea39a4b1433b7"},"schema_version":"1.0","source":{"id":"1401.0719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0719","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0719v1","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0719","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"AVAMH6JMV2QN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AVAMH6JMV2QNOKO4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AVAMH6JM","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:ede7a646401d0a06d230d3dc8a8f6061f2ee3cb2fa0be11417966c8bb33fde5c","target":"graph","created_at":"2026-05-18T03:03:21Z","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 define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.","authors_text":"B.A. Dubrovin, M.V. Pavlov, S.A. Zykov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-01-03T20:59:22Z","title":"Linearly Degenerate Hamiltonian PDEs and a New Class of Solutions to the WDVV Associativity Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0719","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":"sha256:69e128aac04be4ef6dfef000069b4496a7d7c4e17a4462e99b3e1c94b4d67783","target":"record","created_at":"2026-05-18T03:03:21Z","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":"23e37f621fcfd3c3f5cf1d02445f8da40785920ef0522e5bc990edaadec47647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-01-03T20:59:22Z","title_canon_sha256":"7f9c5619aa6fd480013c346f22c8202eec11d8f7f57cecfde81ea39a4b1433b7"},"schema_version":"1.0","source":{"id":"1401.0719","kind":"arxiv","version":1}},"canonical_sha256":"0540c3f92caea0d729dccb73a898d3be451a323161d3158e1a7a9f96e67588a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0540c3f92caea0d729dccb73a898d3be451a323161d3158e1a7a9f96e67588a9","first_computed_at":"2026-05-18T03:03:21.725927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:21.725927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CG1wykJ2sZMbXglIFBorrrB0vQfWEphGp8C+8E3KjXHyezAQayCjFgA3poLbuMxGU1VH8PA7MBra1kVObZ8ABA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:21.726655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69e128aac04be4ef6dfef000069b4496a7d7c4e17a4462e99b3e1c94b4d67783","sha256:ede7a646401d0a06d230d3dc8a8f6061f2ee3cb2fa0be11417966c8bb33fde5c"],"state_sha256":"f366b6e292ecf5980769fee812127d655c097337fc9fe16542c6f02bdfccc010"}