{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XDODMLCJXOTYJAILPKOTYDF6GY","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":"74c171c058e8a559987aa71cb011c77398aaeaa11f3f688d0c978685fd6e5e65","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-12T10:24:52Z","title_canon_sha256":"d25b220f5d3a2d85f7586aa3bdea919892c745fcbbd166cd52fc6ec7fab929da"},"schema_version":"1.0","source":{"id":"1312.3433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3433","created_at":"2026-05-18T01:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3433v2","created_at":"2026-05-18T01:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3433","created_at":"2026-05-18T01:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"XDODMLCJXOTY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XDODMLCJXOTYJAIL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XDODMLCJ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3011ebe4184bdd43df86b34bd9ac0862eda52de90527da47a2cb25f600df2891","target":"graph","created_at":"2026-05-18T01:45:51Z","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":"Let $A,A^*$ be the generators of the $q-$Onsager algebra. Analogues of Lusztig's $r-th$ higher order relations are proposed. In a first part, based on the properties of tridiagonal pairs of $q-$Racah type which satisfy the defining relations of the $q-$Onsager algebra, higher order relations are derived for $r$ generic. The coefficients entering in the relations are determined from a two-variable polynomial generating function. In a second part, it is conjectured that $A,A^*$ satisfy the higher order relations previously obtained. The conjecture is proven for $r=2,3$. For $r$ generic, using an","authors_text":"P. Baseilhac, T.T. Vu","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-12T10:24:52Z","title":"Analogues of Lusztig's higher order relations for the q-Onsager algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3433","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":"sha256:75ff7e24e6249fb326feebda116a892a831b1bcbeec0f98ae91a033827eae5d4","target":"record","created_at":"2026-05-18T01:45:51Z","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":"74c171c058e8a559987aa71cb011c77398aaeaa11f3f688d0c978685fd6e5e65","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-12T10:24:52Z","title_canon_sha256":"d25b220f5d3a2d85f7586aa3bdea919892c745fcbbd166cd52fc6ec7fab929da"},"schema_version":"1.0","source":{"id":"1312.3433","kind":"arxiv","version":2}},"canonical_sha256":"b8dc362c49bba784810b7a9d3c0cbe36338a3e5fb63f37fe10cc67ab4b1f09b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8dc362c49bba784810b7a9d3c0cbe36338a3e5fb63f37fe10cc67ab4b1f09b9","first_computed_at":"2026-05-18T01:45:51.304179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:51.304179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cqAVfyQPvYQsv9EFUdy3rxWTWN7qkK4UWh2oKz9E5IekuLKi+S7ft2LjOfJGI6f46rzMUhhpdIxFdexNJfAmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:51.304752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75ff7e24e6249fb326feebda116a892a831b1bcbeec0f98ae91a033827eae5d4","sha256:3011ebe4184bdd43df86b34bd9ac0862eda52de90527da47a2cb25f600df2891"],"state_sha256":"9166f54f441c2fee50751f750440c3ee88b613373f772b28f0790e54302a6dda"}