{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BTLZV63LZKMXV56T5YA42YKZR3","short_pith_number":"pith:BTLZV63L","schema_version":"1.0","canonical_sha256":"0cd79afb6bca997af7d3ee01cd61598eeb7cea9e21f8654a367f4c15e4031cb5","source":{"kind":"arxiv","id":"2503.05034","version":1},"attestation_state":"computed","paper":{"title":"A New Representation of Ewens-Pitman's Partition Structure and Its Characterization via Riordan Array Sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"stat.ME","authors_text":"Jan Greve","submitted_at":"2025-03-06T23:16:27Z","abstract_excerpt":"Ewens-Pitman's partition structure arises as a system of sampling consistent probability distributions on set partitions induced by the Pitman-Yor process. It is widely used in statistical applications, particularly in species sampling models in Bayesian nonparametrics. Drawing references from the area of representation theory of the infinite symmetric group, we view Ewens-Pitman's partition structure as an example of a non-extreme harmonic function on a branching graph, specifically, the Kingman graph. Taking this perspective enables us to obtain combinatorial and algebraic constructions of t"},"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":"2503.05034","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-03-06T23:16:27Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3edc1716d068e0c84254c85626514578150fb2b55b909204bddeaf29243acaeb","abstract_canon_sha256":"46e6d8af4b2a6074a1f8b5a8e2db0a564af397ed2ce45efad8ee4f28da220ced"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:18.739646Z","signature_b64":"1/CEIwNvHQK/PaxxUdcbYdrSYj5iYqm3P72oy5u2GycyxAk7tgTTHyZtvYAFWS0Xr85x96+d7SF8FJUd8ETABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cd79afb6bca997af7d3ee01cd61598eeb7cea9e21f8654a367f4c15e4031cb5","last_reissued_at":"2026-07-05T10:26:18.738933Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:18.738933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Representation of Ewens-Pitman's Partition Structure and Its Characterization via Riordan Array Sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"stat.ME","authors_text":"Jan Greve","submitted_at":"2025-03-06T23:16:27Z","abstract_excerpt":"Ewens-Pitman's partition structure arises as a system of sampling consistent probability distributions on set partitions induced by the Pitman-Yor process. It is widely used in statistical applications, particularly in species sampling models in Bayesian nonparametrics. Drawing references from the area of representation theory of the infinite symmetric group, we view Ewens-Pitman's partition structure as an example of a non-extreme harmonic function on a branching graph, specifically, the Kingman graph. Taking this perspective enables us to obtain combinatorial and algebraic constructions of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05034","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/2503.05034/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":"2503.05034","created_at":"2026-07-05T10:26:18.739002+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.05034v1","created_at":"2026-07-05T10:26:18.739002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05034","created_at":"2026-07-05T10:26:18.739002+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTLZV63LZKMX","created_at":"2026-07-05T10:26:18.739002+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTLZV63LZKMXV56T","created_at":"2026-07-05T10:26:18.739002+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTLZV63L","created_at":"2026-07-05T10:26:18.739002+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.21128","citing_title":"Named Entity Swapping for Metadata Anonymization in a Text Corpus","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3","json":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3.json","graph_json":"https://pith.science/api/pith-number/BTLZV63LZKMXV56T5YA42YKZR3/graph.json","events_json":"https://pith.science/api/pith-number/BTLZV63LZKMXV56T5YA42YKZR3/events.json","paper":"https://pith.science/paper/BTLZV63L"},"agent_actions":{"view_html":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3","download_json":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3.json","view_paper":"https://pith.science/paper/BTLZV63L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.05034&json=true","fetch_graph":"https://pith.science/api/pith-number/BTLZV63LZKMXV56T5YA42YKZR3/graph.json","fetch_events":"https://pith.science/api/pith-number/BTLZV63LZKMXV56T5YA42YKZR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3/action/storage_attestation","attest_author":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3/action/author_attestation","sign_citation":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3/action/citation_signature","submit_replication":"https://pith.science/pith/BTLZV63LZKMXV56T5YA42YKZR3/action/replication_record"}},"created_at":"2026-07-05T10:26:18.739002+00:00","updated_at":"2026-07-05T10:26:18.739002+00:00"}