{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BIOTOJLWU3YLFBWSAMOPVFMRUP","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":"659df5a6d18571fd788f474a9fe10137838dc18b00f71f60e95a3046e9dba1a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-08T15:47:44Z","title_canon_sha256":"c5b383e649891f71de8f6fea994bd1b7f806711241d967fec7fc14c59e512fd8"},"schema_version":"1.0","source":{"id":"0912.1512","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1512","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1512v4","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1512","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"BIOTOJLWU3YL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BIOTOJLWU3YLFBWS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BIOTOJLW","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:99095d1c5722c6d07ca60ebf4acd515e0011005e8e1719f11ccd6011484470da","target":"graph","created_at":"2026-05-18T00:44:39Z","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 construct a large class of examples of the cyclic sieving phenomenon by expoiting the representation theory of semi-simple Lie algebras. Let $M$ be a finite dimensional representation of a semi-simple Lie algebra and let $B$ be the associated Kashiwara crystal. For $r\\ge 0$, the triple $(X,c,P)$ which exhibits the cyclic sieving phenomenon is constructed as follows: the set $X$ is the set of isolated vertices in the crystal $\\otimes^rB$; the map $c\\colon X\\rightarrow X$ is a generalisation of promotion acting on standard tableaux of rectangular shape and the polynomial $P$ is the fake degre","authors_text":"Bruce W. Westbury","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-08T15:47:44Z","title":"Invariant tensors and the cyclic sieving phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1512","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":"sha256:0868c6dcf7321e3bd5ee42a8f0dbea4790d7fd5bb34ab23aa9b9ba1b2dc4f6ac","target":"record","created_at":"2026-05-18T00:44:39Z","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":"659df5a6d18571fd788f474a9fe10137838dc18b00f71f60e95a3046e9dba1a1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-08T15:47:44Z","title_canon_sha256":"c5b383e649891f71de8f6fea994bd1b7f806711241d967fec7fc14c59e512fd8"},"schema_version":"1.0","source":{"id":"0912.1512","kind":"arxiv","version":4}},"canonical_sha256":"0a1d372576a6f0b286d2031cfa9591a3e83be8d3f7f634481ed70d2f7f153b39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a1d372576a6f0b286d2031cfa9591a3e83be8d3f7f634481ed70d2f7f153b39","first_computed_at":"2026-05-18T00:44:39.231854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:39.231854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7isSI7/BNXVruTxbm8DPYaavnKCpo06vVqW0BNi6FjP1b6+75Om/5yKqTIRQOIKX04UN0SxVuuf8O2sl6iO+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:39.232273Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1512","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0868c6dcf7321e3bd5ee42a8f0dbea4790d7fd5bb34ab23aa9b9ba1b2dc4f6ac","sha256:99095d1c5722c6d07ca60ebf4acd515e0011005e8e1719f11ccd6011484470da"],"state_sha256":"b5d968cb3f7444acb95c2f1ac35b868c928fc4b7d0a3ac8d323c2ba355ba80dc"}