{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4MHEPCX5DYRWIVQNHZSBACRT42","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":"43b4bb8f6e86d6cad50232deea1a89712879b3d42beca21e7bc8e9b33905ad87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-30T02:52:57Z","title_canon_sha256":"8c38f4fbed0e0fc3f25d8a124098a97cea6a7b3b6b84dfc010a6a6ab794befaa"},"schema_version":"1.0","source":{"id":"1810.12500","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12500","created_at":"2026-05-17T23:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12500v2","created_at":"2026-05-17T23:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12500","created_at":"2026-05-17T23:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"4MHEPCX5DYRW","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MHEPCX5DYRWIVQN","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MHEPCX5","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:f4a5fc30b71f6a5241a353ad435141c029bb76b22be4c419abe9d5d093baf965","target":"graph","created_at":"2026-05-17T23:54:15Z","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 the existence, formation and dynamics of gray solitons for an extended quintic nonlinear Schr\\\"odinger (NLS) equation. The considered model finds applications to water waves, when the characteristic parameter $kh$ - where $k$ is the wavenumber and $h$ is the undistorted water's depth - takes the critical value $kh=1.363$. It is shown that this model admits approximate dark soliton solutions emerging from an effective Korteweg-de Vries equation and that two types of gray solitons exist: fast and slow, with the latter being almost stationary objects. Analytical results are corroborated ","authors_text":"D. J. Frantzeskakis, F. Tsitoura, T. P. Horikis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-30T02:52:57Z","title":"Dark solitons for an extended quintic nonlinear Schr\\\"odinger equation: Application to water waves at $kh = 1.363$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12500","kind":"arxiv","version":2},"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":"sha256:7536fca449dabe7015952ccb87dbab40c535a3fcbdc91fd8d48abf313f28cac4","target":"record","created_at":"2026-05-17T23:54:15Z","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":"43b4bb8f6e86d6cad50232deea1a89712879b3d42beca21e7bc8e9b33905ad87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-30T02:52:57Z","title_canon_sha256":"8c38f4fbed0e0fc3f25d8a124098a97cea6a7b3b6b84dfc010a6a6ab794befaa"},"schema_version":"1.0","source":{"id":"1810.12500","kind":"arxiv","version":2}},"canonical_sha256":"e30e478afd1e2364560d3e64100a33e6b656e73ec03c1c4f2b3ebeb34e3890f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e30e478afd1e2364560d3e64100a33e6b656e73ec03c1c4f2b3ebeb34e3890f3","first_computed_at":"2026-05-17T23:54:15.837513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:15.837513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PnDPgfgKBInby/4xkLQnNSCHaqOPld+vlMpYzYSbIz9XOU4s9ieEFoUJ9rH9DbsXmKnDkdbsCZWlCAV6FPLCAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:15.838203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12500","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7536fca449dabe7015952ccb87dbab40c535a3fcbdc91fd8d48abf313f28cac4","sha256:f4a5fc30b71f6a5241a353ad435141c029bb76b22be4c419abe9d5d093baf965"],"state_sha256":"7b3e51a096d7c740fd884312bf212d89d6c64db22b2f5288af46fd06b2981357"}