{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:2R73HVTNYJEOEAPIMTOBYIG5V2","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":"4201dc260106e126f8f5011dfd3e546ff25e47d832eaf85281603ab72aa52082","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-08-25T16:01:28Z","title_canon_sha256":"9af12095ceee3c5294bb96d32bd258271604dd29feb399c0a1f8b039aef1c96e"},"schema_version":"1.0","source":{"id":"2008.11129","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.11129","created_at":"2026-07-05T02:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"2008.11129v6","created_at":"2026-07-05T02:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.11129","created_at":"2026-07-05T02:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"2R73HVTNYJEO","created_at":"2026-07-05T02:18:45Z"},{"alias_kind":"pith_short_16","alias_value":"2R73HVTNYJEOEAPI","created_at":"2026-07-05T02:18:45Z"},{"alias_kind":"pith_short_8","alias_value":"2R73HVTN","created_at":"2026-07-05T02:18:45Z"}],"graph_snapshots":[{"event_id":"sha256:02713c73cd669976b52526f614173d0671cc28414070f8150d764cb9462c02e9","target":"graph","created_at":"2026-07-05T02:18:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.11129/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this note is to compare work of Formanek \\cite{formanek2} on a certain construction of central polynomials with that of Collins \\cite{Coll} on integration on unitary groups.\n  These two quite disjoint topics share the construction of the same function on the symmetric group, which the second author calls {\\em Weingarten function}.\n  By joining these two approaches we succeed in giving a simplified and {\\em very natural} presentation of both Formanek and Collins's Theory.","authors_text":"Claudio Procesi","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-08-25T16:01:28Z","title":"A note on the Weingarten function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.11129","kind":"arxiv","version":6},"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":"sha256:331ced7b8e68f2cbd598c11e736a43ab07eeecdd4a5aa50eca755a74203ba773","target":"record","created_at":"2026-07-05T02:18:45Z","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":"4201dc260106e126f8f5011dfd3e546ff25e47d832eaf85281603ab72aa52082","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-08-25T16:01:28Z","title_canon_sha256":"9af12095ceee3c5294bb96d32bd258271604dd29feb399c0a1f8b039aef1c96e"},"schema_version":"1.0","source":{"id":"2008.11129","kind":"arxiv","version":6}},"canonical_sha256":"d47fb3d66dc248e201e864dc1c20ddae9b86627812eaa853b245a71205f9f7a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d47fb3d66dc248e201e864dc1c20ddae9b86627812eaa853b245a71205f9f7a2","first_computed_at":"2026-07-05T02:18:45.134131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:18:45.134131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UsgGU72vy+GK5zQanT/BioB/HP4ftWni1NRlnv4o3MuvsuFeh6a0fyo6OvNM9TTL3c8uiIIZTtess1Q45KXNDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:18:45.134634Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.11129","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:331ced7b8e68f2cbd598c11e736a43ab07eeecdd4a5aa50eca755a74203ba773","sha256:02713c73cd669976b52526f614173d0671cc28414070f8150d764cb9462c02e9"],"state_sha256":"de516d9cbb6c9462bdc47ba5c63ae207121bccce35c0e02a6be8afb5b4dc394d"}