{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z2YI464U7JMVUWHQRG3GZEH5VQ","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":"9696000e62003b4c11c83670480f5c6742a0756319de801921f913e8438643fa","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-26T22:33:51Z","title_canon_sha256":"3b66c3725b6d6259a4422d506b7fe9c6d77f7aa9e3da23d819ca47fb63d11726"},"schema_version":"1.0","source":{"id":"1106.5277","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5277","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5277v2","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5277","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"Z2YI464U7JMV","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z2YI464U7JMVUWHQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z2YI464U","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:b30476c4ad7ff40e6d2a9d065b03c37c8a0a3fbf9d5510bddd859521ea76792e","target":"graph","created_at":"2026-05-18T03:20:35Z","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 introduce an associative algebra $\\M_k(x)$ whose dimension is the $2k$-th Motzkin number. The algebra $\\M_k(x)$ has a basis of \"Motzkin diagrams,\" which are analogous to Brauer and Temperley-Lieb diagrams, and it contains the Temperley-Lieb algebra $\\TL_k(x)$ as a subalgebra. We prove that for a particular value of $x$, the algebra $\\M_k(x)$ is the centralizer algebra of $\\uqsl$ acting on the $k$-fold tensor power of the sum of the 1-dimensional and 2-dimensional irreducible $\\uqsl$-modules. We show that $\\M_k(x)$ is generated by special diagrams $\\ell_i, t_i, r_i \\ (1 \\le i < k)$ and $p_j ","authors_text":"Georgia Benkart, Tom Halverson","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-26T22:33:51Z","title":"Motzkin Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5277","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:a35953f5db09ff28560c50f879edc112b2e96daccd4f3e9d25d597636585bb74","target":"record","created_at":"2026-05-18T03:20:35Z","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":"9696000e62003b4c11c83670480f5c6742a0756319de801921f913e8438643fa","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-26T22:33:51Z","title_canon_sha256":"3b66c3725b6d6259a4422d506b7fe9c6d77f7aa9e3da23d819ca47fb63d11726"},"schema_version":"1.0","source":{"id":"1106.5277","kind":"arxiv","version":2}},"canonical_sha256":"ceb08e7b94fa595a58f089b66c90fdac1faf6436dabfe6fd5c413bf09b9ed0e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceb08e7b94fa595a58f089b66c90fdac1faf6436dabfe6fd5c413bf09b9ed0e2","first_computed_at":"2026-05-18T03:20:35.839486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:35.839486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eQZSMGIjgLfdDm3nhpjIys5As54jZDlCqv051H9rrLgdhBCcw3ODqPdY9P6TkfiebIeg82Dc3pgstRfpJ16sAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:35.840270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5277","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a35953f5db09ff28560c50f879edc112b2e96daccd4f3e9d25d597636585bb74","sha256:b30476c4ad7ff40e6d2a9d065b03c37c8a0a3fbf9d5510bddd859521ea76792e"],"state_sha256":"e89cb7683cb8efaaef38229d32cc90b4dedbdcd9ea0473cdcc07438267fe2d3a"}