{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VSYPTR5SKQEOH2CFVXWXVOEW3I","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":"f8d066863c1e8b6158f2ef327474031f141f16c8dfcaddf5ec79710e224477f5","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-22T13:26:41Z","title_canon_sha256":"dccd72a1ccdf08a34d175d9360b67505b27ce57579ca798cdda9b6aecef5399c"},"schema_version":"1.0","source":{"id":"1205.4910","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4910","created_at":"2026-05-18T01:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4910v3","created_at":"2026-05-18T01:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4910","created_at":"2026-05-18T01:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"VSYPTR5SKQEO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VSYPTR5SKQEOH2CF","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VSYPTR5S","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:4b94b582027c17cdcba1a062b96991b8a0e5445a90715602977712a41482c6f8","target":"graph","created_at":"2026-05-18T01:57:24Z","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":"In this paper we construct Yang-Baxter (YB) maps using Darboux matrices which are invariant under the action of finite reduction groups. We present 6-dimensional YB maps corresponding to Darboux transformations for the Nonlinear Schr\\\"odinger (NLS) equation and the derivative Nonlinear Schr\\\"odinger (DNLS) equation. These YB maps can be restricted to $4-$dimensional YB maps on invariant leaves. The former are completely integrable and they also have applications to a recent theory of maps preserving functions with symmetries \\cite{Allan-Pavlos}. We give a $6-$ dimensional YB-map corresponding ","authors_text":"Alexander Mikhailov, Sotiris Konstantinou-Rizos","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-22T13:26:41Z","title":"Darboux transformations, finite reduction groups and related Yang-Baxter maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4910","kind":"arxiv","version":3},"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":"sha256:1be48380635727be81bd22622b54ab72844094f1cc89b62e2ebe1880d4a9e020","target":"record","created_at":"2026-05-18T01:57:24Z","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":"f8d066863c1e8b6158f2ef327474031f141f16c8dfcaddf5ec79710e224477f5","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-22T13:26:41Z","title_canon_sha256":"dccd72a1ccdf08a34d175d9360b67505b27ce57579ca798cdda9b6aecef5399c"},"schema_version":"1.0","source":{"id":"1205.4910","kind":"arxiv","version":3}},"canonical_sha256":"acb0f9c7b25408e3e845aded7ab896da038f1729f8ec2d41ec2b4c360d56b819","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acb0f9c7b25408e3e845aded7ab896da038f1729f8ec2d41ec2b4c360d56b819","first_computed_at":"2026-05-18T01:57:24.501192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:24.501192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EAdwbixY91Iuv9zZH6Yf7Oal/UlMOJJy/pAtgdzbT5X5WCjRB6FQxmQqgm8PYUcf+xlu49h8JHegcDkARYD0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:24.501664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4910","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be48380635727be81bd22622b54ab72844094f1cc89b62e2ebe1880d4a9e020","sha256:4b94b582027c17cdcba1a062b96991b8a0e5445a90715602977712a41482c6f8"],"state_sha256":"bdce86aff4ec0943ababfac63081df72c1d9595b7dbd1a9aee967e4f440ce194"}