{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VLIRUD4TPSRJOHAKMR6WSNL2KY","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":"6b98a39ee0bdce5390ab09bcbdaef4852db87ebec238ac15347ef3862313e077","cross_cats_sorted":["math-ph","math.CA","math.CO","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2022-12-07T14:50:54Z","title_canon_sha256":"b29e12a38d6d9cd5cc4fefbf75ae00e69cf074cf2c71a293027e0dbedbb4d588"},"schema_version":"1.0","source":{"id":"2212.03679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.03679","created_at":"2026-07-05T07:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"2212.03679v2","created_at":"2026-07-05T07:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.03679","created_at":"2026-07-05T07:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"VLIRUD4TPSRJ","created_at":"2026-07-05T07:25:38Z"},{"alias_kind":"pith_short_16","alias_value":"VLIRUD4TPSRJOHAK","created_at":"2026-07-05T07:25:38Z"},{"alias_kind":"pith_short_8","alias_value":"VLIRUD4T","created_at":"2026-07-05T07:25:38Z"}],"graph_snapshots":[{"event_id":"sha256:89e3b5625fac0866cb071603a473be718855f8195865de3a92b7b87f2b38904d","target":"graph","created_at":"2026-07-05T07:25:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.03679/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The full Kostant-Toda (f-KT) lattice is a natural generalization of the classical tridiagonal Toda lattice. We study singular structure of solutions of the f-KT lattices defined on simple Lie algebras in two different ways: through the $\\tau$-functions and through the Kowalevski-Painlev\\'e analysis. The $\\tau$-function formalism relies on and is equivalent to the representation theory of the underlying Lie algebras, while the Kowalevski-Painlev\\'e analysis is representation independent and we are able to characterize all the terms in the Laurent series solutions of the f-KT lattices via the st","authors_text":"Yuancheng Xie","cross_cats":["math-ph","math.CA","math.CO","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2022-12-07T14:50:54Z","title":"On the full Kostant-Toda lattice and the flag varieties. I. The singular solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.03679","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:b052f3b3444718b7b71f0291a60388277378e656f629f0f4119eedfe6280a7fc","target":"record","created_at":"2026-07-05T07:25:38Z","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":"6b98a39ee0bdce5390ab09bcbdaef4852db87ebec238ac15347ef3862313e077","cross_cats_sorted":["math-ph","math.CA","math.CO","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2022-12-07T14:50:54Z","title_canon_sha256":"b29e12a38d6d9cd5cc4fefbf75ae00e69cf074cf2c71a293027e0dbedbb4d588"},"schema_version":"1.0","source":{"id":"2212.03679","kind":"arxiv","version":2}},"canonical_sha256":"aad11a0f937ca2971c0a647d69357a560dc7976637108b632e6e05924c6857ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aad11a0f937ca2971c0a647d69357a560dc7976637108b632e6e05924c6857ff","first_computed_at":"2026-07-05T07:25:38.630335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:25:38.630335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YECdtTX5HtRzBmquwKIsahEvO5ZcIOkCPPTkJszTwerj2QqU4UhCD+fv7g3g8QzWOSr9XeVmKHdshIcjpeoQCw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:25:38.630841Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.03679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b052f3b3444718b7b71f0291a60388277378e656f629f0f4119eedfe6280a7fc","sha256:89e3b5625fac0866cb071603a473be718855f8195865de3a92b7b87f2b38904d"],"state_sha256":"21a7b7ffa1b10101201a4482daf61443151741fad1c0145e520405df0cc525e0"}