{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WFPVTXY4EKLQODKZEGZZ4E67AU","short_pith_number":"pith:WFPVTXY4","canonical_record":{"source":{"id":"1204.5117","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T17:16:24Z","cross_cats_sorted":["math.CO","math.MP","math.QA","math.RT"],"title_canon_sha256":"7fe2137bf0b3c8d7a70ba64f3c159220ed7c875e66f3c4873aeacca1046bcddb","abstract_canon_sha256":"a22f665f2d586fffaea60cb24cff9d1be5af3675cf5f608ba1e9339ba8aa0ae1"},"schema_version":"1.0"},"canonical_sha256":"b15f59df1c2297070d5921b39e13df053b5690afa4806cf4c008755abecba63d","source":{"kind":"arxiv","id":"1204.5117","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5117","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5117v4","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5117","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"WFPVTXY4EKLQ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WFPVTXY4EKLQODKZ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WFPVTXY4","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WFPVTXY4EKLQODKZEGZZ4E67AU","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5117","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T17:16:24Z","cross_cats_sorted":["math.CO","math.MP","math.QA","math.RT"],"title_canon_sha256":"7fe2137bf0b3c8d7a70ba64f3c159220ed7c875e66f3c4873aeacca1046bcddb","abstract_canon_sha256":"a22f665f2d586fffaea60cb24cff9d1be5af3675cf5f608ba1e9339ba8aa0ae1"},"schema_version":"1.0"},"canonical_sha256":"b15f59df1c2297070d5921b39e13df053b5690afa4806cf4c008755abecba63d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:45.323912Z","signature_b64":"HuYx3k94kflaoM9kb43sS5/p7Exf0F1GrLZT4ax1zu4o0o0MWdAmogSffhDjNVchbkx0yWfQpV9m+tXEiwiaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b15f59df1c2297070d5921b39e13df053b5690afa4806cf4c008755abecba63d","last_reissued_at":"2026-05-18T03:32:45.323042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:45.323042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5117","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":"2026-05-18T03:32:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ybgYVU1UTHExmlNX9yld3TjeM6RSIDvddOudinPSwTQyiRcJzayIUKDnDYUrZgDCxN17bjObf5cKpW+5fPPzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:42:36.392804Z"},"content_sha256":"2193f60a4bb417d3174beffb4351ead684e90a57d66baa1eeb46cee0a52ebf3d","schema_version":"1.0","event_id":"sha256:2193f60a4bb417d3174beffb4351ead684e90a57d66baa1eeb46cee0a52ebf3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WFPVTXY4EKLQODKZEGZZ4E67AU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clustering properties of rectangular Macdonald polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"Charles F. Dunkl, Jean-Gabriel Luque","submitted_at":"2012-04-23T17:16:24Z","abstract_excerpt":"The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials. The present paper is devoted to the proof of this formula. To this aim we use four families of Jack/Macdonald polynomials: symmetric homogeneous, nonsymmetric homogeneous, shifted symmetric and shifted nonsymmetric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5117","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":"2026-05-18T03:32:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0wVIa9bq+MeqxNPD/KfLDQB5HDnSSoWDGKnVBjKgiDtwGgD9A0Deuju7ZnoIW9q7zztBEWX2xQo1wHXus+3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:42:36.393226Z"},"content_sha256":"45a5379f3c7708b4c969607e4973c14c1d343fb52bf467ce6b7cf88b18d3fa8b","schema_version":"1.0","event_id":"sha256:45a5379f3c7708b4c969607e4973c14c1d343fb52bf467ce6b7cf88b18d3fa8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFPVTXY4EKLQODKZEGZZ4E67AU/bundle.json","state_url":"https://pith.science/pith/WFPVTXY4EKLQODKZEGZZ4E67AU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFPVTXY4EKLQODKZEGZZ4E67AU/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":"2026-06-12T02:42:36Z","links":{"resolver":"https://pith.science/pith/WFPVTXY4EKLQODKZEGZZ4E67AU","bundle":"https://pith.science/pith/WFPVTXY4EKLQODKZEGZZ4E67AU/bundle.json","state":"https://pith.science/pith/WFPVTXY4EKLQODKZEGZZ4E67AU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFPVTXY4EKLQODKZEGZZ4E67AU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WFPVTXY4EKLQODKZEGZZ4E67AU","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":"a22f665f2d586fffaea60cb24cff9d1be5af3675cf5f608ba1e9339ba8aa0ae1","cross_cats_sorted":["math.CO","math.MP","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T17:16:24Z","title_canon_sha256":"7fe2137bf0b3c8d7a70ba64f3c159220ed7c875e66f3c4873aeacca1046bcddb"},"schema_version":"1.0","source":{"id":"1204.5117","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5117","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5117v4","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5117","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"WFPVTXY4EKLQ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WFPVTXY4EKLQODKZ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WFPVTXY4","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:45a5379f3c7708b4c969607e4973c14c1d343fb52bf467ce6b7cf88b18d3fa8b","target":"graph","created_at":"2026-05-18T03:32:45Z","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":"The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials. The present paper is devoted to the proof of this formula. To this aim we use four families of Jack/Macdonald polynomials: symmetric homogeneous, nonsymmetric homogeneous, shifted symmetric and shifted nonsymmetric.","authors_text":"Charles F. Dunkl, Jean-Gabriel Luque","cross_cats":["math.CO","math.MP","math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T17:16:24Z","title":"Clustering properties of rectangular Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5117","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":"sha256:2193f60a4bb417d3174beffb4351ead684e90a57d66baa1eeb46cee0a52ebf3d","target":"record","created_at":"2026-05-18T03:32:45Z","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":"a22f665f2d586fffaea60cb24cff9d1be5af3675cf5f608ba1e9339ba8aa0ae1","cross_cats_sorted":["math.CO","math.MP","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-23T17:16:24Z","title_canon_sha256":"7fe2137bf0b3c8d7a70ba64f3c159220ed7c875e66f3c4873aeacca1046bcddb"},"schema_version":"1.0","source":{"id":"1204.5117","kind":"arxiv","version":4}},"canonical_sha256":"b15f59df1c2297070d5921b39e13df053b5690afa4806cf4c008755abecba63d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b15f59df1c2297070d5921b39e13df053b5690afa4806cf4c008755abecba63d","first_computed_at":"2026-05-18T03:32:45.323042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:45.323042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HuYx3k94kflaoM9kb43sS5/p7Exf0F1GrLZT4ax1zu4o0o0MWdAmogSffhDjNVchbkx0yWfQpV9m+tXEiwiaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:45.323912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5117","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2193f60a4bb417d3174beffb4351ead684e90a57d66baa1eeb46cee0a52ebf3d","sha256:45a5379f3c7708b4c969607e4973c14c1d343fb52bf467ce6b7cf88b18d3fa8b"],"state_sha256":"9e4d5edca3552161f5638c21726a2d510a18f9c58ba4124413675fe86f7ae474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JwJRVpDyr+KeSgOVVIUq1ZlbJTbWBO9cGhSKvNzgaw5qiMCdqglTYKJ2Ijf1rDPIXAMnjd2EVQ+G73a7oR17BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:42:36.396262Z","bundle_sha256":"063f5480583189a5aef10eb601359de98178fafc05d79e633cfa70ae21bd9f3a"}}