{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NDOSH27KCMPZXWQD7HVPSDMDK2","short_pith_number":"pith:NDOSH27K","schema_version":"1.0","canonical_sha256":"68dd23ebea131f9bda03f9eaf90d83569f41d191d16dcef066c3bc42d63e7c4f","source":{"kind":"arxiv","id":"2505.08394","version":1},"attestation_state":"computed","paper":{"title":"Probability measures on families of partitions related to harmonic analysis on big wreath products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.RT","authors_text":"Eugene Strahov","submitted_at":"2025-05-13T09:44:45Z","abstract_excerpt":"We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called the $z$-measures for the wreath product of a compact group with the symmetric group in the present paper. Our main result is an explicit formula for these $z$-measures which holds true for an arbitrary compact group. The result enables us to describe the spectral measures of the generalized regular representations of big wreath products."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.08394","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-13T09:44:45Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"79fce56580caf7c7d72aa97293c685cf299af944db80f0caee074b2b295fc96e","abstract_canon_sha256":"8ac0629b2aa8357b618c5b433624f0d3be50e0b6122dbdefb7de181d9cb967a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:05.888507Z","signature_b64":"41IgVQPkI+1r2SL+tDFdgsdHyITKPm/YspSeA9TpYeHtKvucRklTzZQTAh3iEkHtS+5lppd0rz3XVZ2Gh4khBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68dd23ebea131f9bda03f9eaf90d83569f41d191d16dcef066c3bc42d63e7c4f","last_reissued_at":"2026-06-02T02:04:05.888070Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:05.888070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probability measures on families of partitions related to harmonic analysis on big wreath products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.RT","authors_text":"Eugene Strahov","submitted_at":"2025-05-13T09:44:45Z","abstract_excerpt":"We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called the $z$-measures for the wreath product of a compact group with the symmetric group in the present paper. Our main result is an explicit formula for these $z$-measures which holds true for an arbitrary compact group. The result enables us to describe the spectral measures of the generalized regular representations of big wreath products."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08394","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.08394/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.08394","created_at":"2026-06-02T02:04:05.888121+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.08394v1","created_at":"2026-06-02T02:04:05.888121+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.08394","created_at":"2026-06-02T02:04:05.888121+00:00"},{"alias_kind":"pith_short_12","alias_value":"NDOSH27KCMPZ","created_at":"2026-06-02T02:04:05.888121+00:00"},{"alias_kind":"pith_short_16","alias_value":"NDOSH27KCMPZXWQD","created_at":"2026-06-02T02:04:05.888121+00:00"},{"alias_kind":"pith_short_8","alias_value":"NDOSH27K","created_at":"2026-06-02T02:04:05.888121+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.20857","citing_title":"Evo-Memory: Benchmarking LLM Agent Test-time Learning with Self-Evolving Memory","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2","json":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2.json","graph_json":"https://pith.science/api/pith-number/NDOSH27KCMPZXWQD7HVPSDMDK2/graph.json","events_json":"https://pith.science/api/pith-number/NDOSH27KCMPZXWQD7HVPSDMDK2/events.json","paper":"https://pith.science/paper/NDOSH27K"},"agent_actions":{"view_html":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2","download_json":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2.json","view_paper":"https://pith.science/paper/NDOSH27K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.08394&json=true","fetch_graph":"https://pith.science/api/pith-number/NDOSH27KCMPZXWQD7HVPSDMDK2/graph.json","fetch_events":"https://pith.science/api/pith-number/NDOSH27KCMPZXWQD7HVPSDMDK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2/action/storage_attestation","attest_author":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2/action/author_attestation","sign_citation":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2/action/citation_signature","submit_replication":"https://pith.science/pith/NDOSH27KCMPZXWQD7HVPSDMDK2/action/replication_record"}},"created_at":"2026-06-02T02:04:05.888121+00:00","updated_at":"2026-06-02T02:04:05.888121+00:00"}