{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TWGVV543G2GFBZSYTE3A7BLC6I","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":"9e8e2f9e60fdd5e0cfcec96bf7dbfdd2b1ab1c8ce0322bfcce544f2094b63bd4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-09-08T10:57:52Z","title_canon_sha256":"3db353473d10f23e3179a3aa062cd234b5d0ce8965a60240579cf9c0d31d41a3"},"schema_version":"1.0","source":{"id":"1109.1689","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1689","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1689v4","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1689","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"TWGVV543G2GF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TWGVV543G2GFBZSY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TWGVV543","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6418358a5ee1f957c1ab3e359a8b28fafbb2eaa9c4df1b1d76858fb841494a9a","target":"graph","created_at":"2026-05-18T03:45:23Z","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":"Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras $A_N$, $B_N$, $C_N$, $G_2$, $D_3$, $A_1^{(1)}$, $A_2^{(2)}$, $D^{(2)}_N$ these systems are proved to be integrable. For the systems corresponding to the algebras $A_2$, $A_1^{(1)}$, $A_2^{(2)}$ generalized symmetries are found. For the systems $A_2$, $B_2$, $C_2$, $G_2$, $D_3$ complete sets of independent integrals are found. The Lax representation for the difference-difference systems corresponding to $A_N$, $B_N$, $C_N$, $A^{(1)}_1$, $D^{(2)}_N$ a","authors_text":"Ismagil Habibullin, Marina Yangubaeva, Rustem Garifullin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-09-08T10:57:52Z","title":"Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1689","kind":"arxiv","version":4},"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":"sha256:4834a3dbae64bbc67fa87c70a9daa34e97c4b6198e7aa27c8554e215b94ddc7c","target":"record","created_at":"2026-05-18T03:45:23Z","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":"9e8e2f9e60fdd5e0cfcec96bf7dbfdd2b1ab1c8ce0322bfcce544f2094b63bd4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.SI","submitted_at":"2011-09-08T10:57:52Z","title_canon_sha256":"3db353473d10f23e3179a3aa062cd234b5d0ce8965a60240579cf9c0d31d41a3"},"schema_version":"1.0","source":{"id":"1109.1689","kind":"arxiv","version":4}},"canonical_sha256":"9d8d5af79b368c50e65899360f8562f2039a2b75277dd7bc6119e955b66013d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d8d5af79b368c50e65899360f8562f2039a2b75277dd7bc6119e955b66013d6","first_computed_at":"2026-05-18T03:45:23.233441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:23.233441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XcvCpSf4DDVYP2AGoslNpa10yrUssaP79syAaIehmU/RVjYxYtdPIIzZcb8mQUCVoRZnCDZX3phUZV8WbR1NCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:23.233823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1689","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4834a3dbae64bbc67fa87c70a9daa34e97c4b6198e7aa27c8554e215b94ddc7c","sha256:6418358a5ee1f957c1ab3e359a8b28fafbb2eaa9c4df1b1d76858fb841494a9a"],"state_sha256":"951c232c4d83ca5fc8986c02c7400cf43d2a2ce5f43c7b3ab863211305adc6fb"}