{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3IMWXH5KI6WSYEMYHWY7D5KVAX","short_pith_number":"pith:3IMWXH5K","canonical_record":{"source":{"id":"1009.2366","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2010-09-13T12:36:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"f76a79f3f5d6711d7c8f02b576f45062a2b4e50a6af50c8f45fe44ff0b373df2","abstract_canon_sha256":"972564387a1df395f514a7b1124dde95159d7057c4116575e8de9c555470d5a7"},"schema_version":"1.0"},"canonical_sha256":"da196b9faa47ad2c11983db1f1f55505cc6ab897fbf482eff1a3ae5a5000e3f4","source":{"kind":"arxiv","id":"1009.2366","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2366","created_at":"2026-05-18T04:26:45Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2366v4","created_at":"2026-05-18T04:26:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2366","created_at":"2026-05-18T04:26:45Z"},{"alias_kind":"pith_short_12","alias_value":"3IMWXH5KI6WS","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3IMWXH5KI6WSYEMY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3IMWXH5K","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3IMWXH5KI6WSYEMYHWY7D5KVAX","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2366","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2010-09-13T12:36:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"f76a79f3f5d6711d7c8f02b576f45062a2b4e50a6af50c8f45fe44ff0b373df2","abstract_canon_sha256":"972564387a1df395f514a7b1124dde95159d7057c4116575e8de9c555470d5a7"},"schema_version":"1.0"},"canonical_sha256":"da196b9faa47ad2c11983db1f1f55505cc6ab897fbf482eff1a3ae5a5000e3f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:45.453569Z","signature_b64":"/BD54HLMMs0k/8CVNHEWJIRk/FtdmqX8OrXgbo2a9tfZngdsmCoPcK9TkKawxwHexWChwhvTtmY7QRsaeCUeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da196b9faa47ad2c11983db1f1f55505cc6ab897fbf482eff1a3ae5a5000e3f4","last_reissued_at":"2026-05-18T04:26:45.452889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:45.452889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2366","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oYUGM1GCcoIUnQqu22R8SQ2VhnIf+HkdQ0vFpdazViKqOM05oy+aHBN4Vv1uxV6L5zRpkjBXTxVEPvkhVLAJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:12:35.705350Z"},"content_sha256":"796514eeeb56918f1f9c0af29f24c57005a602922150a30be388d8541344af09","schema_version":"1.0","event_id":"sha256:796514eeeb56918f1f9c0af29f24c57005a602922150a30be388d8541344af09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3IMWXH5KI6WSYEMYHWY7D5KVAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector-Valued Jack Polynomials from Scratch","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Charles F. Dunkl, Jean-Gabriel Luque","submitted_at":"2010-09-13T12:36:48Z","abstract_excerpt":"Vector-valued Jack polynomials associated to the symmetric group ${\\mathfrak S}_N$ are polynomials with multiplicities in an irreducible module of ${\\mathfrak S}_N$ and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups $G(r,p,N)$ and studied by one of the authors (C. Dunkl) in the specialization $r=p=1$ (i.e. for the symmetric group). By adapting a construction due to Lascoux, we describe an algorithm allowi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2366","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfmIowX5CSvCm2cXPPUinfTmkgegMjsL5RoHukjiua37al/2xreFnjI6FB1Sq/DXEA7ittrv/ac0VSPuPLkWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:12:35.705930Z"},"content_sha256":"270053415baded71b7f8f5ad73229f8b671283ada47d24a45e160201c677dd61","schema_version":"1.0","event_id":"sha256:270053415baded71b7f8f5ad73229f8b671283ada47d24a45e160201c677dd61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX/bundle.json","state_url":"https://pith.science/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T18:12:35Z","links":{"resolver":"https://pith.science/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX","bundle":"https://pith.science/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX/bundle.json","state":"https://pith.science/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IMWXH5KI6WSYEMYHWY7D5KVAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3IMWXH5KI6WSYEMYHWY7D5KVAX","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":"972564387a1df395f514a7b1124dde95159d7057c4116575e8de9c555470d5a7","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2010-09-13T12:36:48Z","title_canon_sha256":"f76a79f3f5d6711d7c8f02b576f45062a2b4e50a6af50c8f45fe44ff0b373df2"},"schema_version":"1.0","source":{"id":"1009.2366","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2366","created_at":"2026-05-18T04:26:45Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2366v4","created_at":"2026-05-18T04:26:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2366","created_at":"2026-05-18T04:26:45Z"},{"alias_kind":"pith_short_12","alias_value":"3IMWXH5KI6WS","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3IMWXH5KI6WSYEMY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3IMWXH5K","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:270053415baded71b7f8f5ad73229f8b671283ada47d24a45e160201c677dd61","target":"graph","created_at":"2026-05-18T04:26:45Z","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":"Vector-valued Jack polynomials associated to the symmetric group ${\\mathfrak S}_N$ are polynomials with multiplicities in an irreducible module of ${\\mathfrak S}_N$ and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups $G(r,p,N)$ and studied by one of the authors (C. Dunkl) in the specialization $r=p=1$ (i.e. for the symmetric group). By adapting a construction due to Lascoux, we describe an algorithm allowi","authors_text":"Charles F. Dunkl, Jean-Gabriel Luque","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2010-09-13T12:36:48Z","title":"Vector-Valued Jack Polynomials from Scratch"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2366","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":"sha256:796514eeeb56918f1f9c0af29f24c57005a602922150a30be388d8541344af09","target":"record","created_at":"2026-05-18T04:26:45Z","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":"972564387a1df395f514a7b1124dde95159d7057c4116575e8de9c555470d5a7","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2010-09-13T12:36:48Z","title_canon_sha256":"f76a79f3f5d6711d7c8f02b576f45062a2b4e50a6af50c8f45fe44ff0b373df2"},"schema_version":"1.0","source":{"id":"1009.2366","kind":"arxiv","version":4}},"canonical_sha256":"da196b9faa47ad2c11983db1f1f55505cc6ab897fbf482eff1a3ae5a5000e3f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da196b9faa47ad2c11983db1f1f55505cc6ab897fbf482eff1a3ae5a5000e3f4","first_computed_at":"2026-05-18T04:26:45.452889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:45.452889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/BD54HLMMs0k/8CVNHEWJIRk/FtdmqX8OrXgbo2a9tfZngdsmCoPcK9TkKawxwHexWChwhvTtmY7QRsaeCUeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:45.453569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2366","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:796514eeeb56918f1f9c0af29f24c57005a602922150a30be388d8541344af09","sha256:270053415baded71b7f8f5ad73229f8b671283ada47d24a45e160201c677dd61"],"state_sha256":"f597b1fe83efbd6b69ad57448cc183f1873a8e618149531494c34b0a150ac701"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CpAMgUcYRoXOxhswqRjc6ho5RzUV51tMSWfw+prrh+tGkLQ6CaYTgNflPisYhP/ij75QfZphlr2UuI2cJzDRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:12:35.708453Z","bundle_sha256":"fb3205bce6fab4844594764ad3d1ea07422c75122a218ca44575e09f2b549dd4"}}