{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XRZFERI7UAESITJJMEAGIZI3RY","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":"89542e2508c15c4ce445e612a9b05fa9e2e63ec56fa7769e52e294bba3272fcf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-27T09:44:55Z","title_canon_sha256":"8a2ff36f4c67a62f689de71fabf7e2362db89f2ed1a63ee349584b5927be4b68"},"schema_version":"1.0","source":{"id":"1106.5339","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5339","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5339v7","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5339","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"XRZFERI7UAES","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XRZFERI7UAESITJJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XRZFERI7","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:c08e7d7b536346588459bd32f71bc3f7f06f20a5f4c6ca82f4de36718cbcddb9","target":"graph","created_at":"2026-05-18T02:19:42Z","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 define a method which produces explicit cellular bases for algebras obtained via a Jones basic construction. For the class of algebras in question, our method gives formulas for generic Murphy--type cellular bases indexed by paths on branching diagrams and compatible with restriction and induction on cell modules. The construction given here allows for a uniform combinatorial treatment of cellular bases and representations of the Brauer, Birman-Murakami-Wenzl, Temperley-Lieb, and partition algebras, among others.","authors_text":"Frederick M. Goodman, John Enyang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-27T09:44:55Z","title":"Cellular bases for algebras with a Jones basic construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5339","kind":"arxiv","version":7},"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:c0e68ce765664625bc1f1a752d763236230a08fa348942c7c07afd52a0fb202f","target":"record","created_at":"2026-05-18T02:19:42Z","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":"89542e2508c15c4ce445e612a9b05fa9e2e63ec56fa7769e52e294bba3272fcf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-27T09:44:55Z","title_canon_sha256":"8a2ff36f4c67a62f689de71fabf7e2362db89f2ed1a63ee349584b5927be4b68"},"schema_version":"1.0","source":{"id":"1106.5339","kind":"arxiv","version":7}},"canonical_sha256":"bc7252451fa009244d29610064651b8e1a774961cba66d6f9ae71ec5f5d86197","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc7252451fa009244d29610064651b8e1a774961cba66d6f9ae71ec5f5d86197","first_computed_at":"2026-05-18T02:19:42.873721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:42.873721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xj17p/akuATGT1IrWdv4gVexU0blpcU2bD02bLfeg/AVQ+EdhGGEH75PBdVmApS0oEUj5/LD9YabB3OO73oqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:42.874232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5339","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0e68ce765664625bc1f1a752d763236230a08fa348942c7c07afd52a0fb202f","sha256:c08e7d7b536346588459bd32f71bc3f7f06f20a5f4c6ca82f4de36718cbcddb9"],"state_sha256":"d477b543ece330a45569e2b81d0dfb4e69e93ad80695673a8499b1d646a4cc96"}