{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3EQNFIWVGTI2BEFNTFIGSGZ3NT","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":"0c5bce946dc57fd2bc848ce30cb28b809528d07449cff07e3a5fd56e0a6d0ed9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-06T18:07:38Z","title_canon_sha256":"7b7bf786eeff865486aa5ea9bc01c579f2fea621a2ca7f1b1fb575928e008383"},"schema_version":"1.0","source":{"id":"1902.02310","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02310","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02310v1","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02310","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"3EQNFIWVGTI2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3EQNFIWVGTI2BEFN","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3EQNFIWV","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:dc5f817afbad6eba7bfb490929ae925890be36ec5487166eb11a4cec56fb174c","target":"graph","created_at":"2026-05-17T23:54:37Z","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":"For each partition $\\tau$ of $N$ there are irreducible modules of the symmetric groups $\\mathcal{S}_{N}$ or the corresponding Hecke algebra $\\mathcal{H}_{N}\\left( t\\right) $ whose bases consist of reverse standard Young tableaux of shape $\\tau$. There are associated spaces of nonsymmetric Jack and Macdonald polynomials taking values in these modules, respectively.The Jack polynomials are a special case of those constructed by Griffeth for the infinite family $G\\left( n,p,N\\right) $ of complex reflection groups. The Macdonald polynomials were constructed by Luque and the author. For both the gr","authors_text":"Charles F. Dunkl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-06T18:07:38Z","title":"Some Singular Vector-valued Jack and Macdonald Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02310","kind":"arxiv","version":1},"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":"sha256:77e13b2c19adcc4bb2dce59564039bf94d3c67cbce36f23592c44802ba3102c8","target":"record","created_at":"2026-05-17T23:54:37Z","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":"0c5bce946dc57fd2bc848ce30cb28b809528d07449cff07e3a5fd56e0a6d0ed9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-06T18:07:38Z","title_canon_sha256":"7b7bf786eeff865486aa5ea9bc01c579f2fea621a2ca7f1b1fb575928e008383"},"schema_version":"1.0","source":{"id":"1902.02310","kind":"arxiv","version":1}},"canonical_sha256":"d920d2a2d534d1a090ad9950691b3b6ccbd80639c6bbc6a1219fbc606a2367b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d920d2a2d534d1a090ad9950691b3b6ccbd80639c6bbc6a1219fbc606a2367b3","first_computed_at":"2026-05-17T23:54:37.362586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:37.362586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PgCLcpMZaDpKTWeCu1C7LjwlylcKnR64OjuyAltZHuiMHnDRvRB4sCFMpKbS5pJeWJqbWigPoj4ZkWGLZK3WCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:37.363311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02310","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77e13b2c19adcc4bb2dce59564039bf94d3c67cbce36f23592c44802ba3102c8","sha256:dc5f817afbad6eba7bfb490929ae925890be36ec5487166eb11a4cec56fb174c"],"state_sha256":"64464577a99e5f7ae1a3c11c34393f8ef829be84f5fc1a3c1642cd60086a039f"}