{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ZOYEXYCXWJUFZULFRDRNRHYYIK","short_pith_number":"pith:ZOYEXYCX","schema_version":"1.0","canonical_sha256":"cbb04be057b2685cd16588e2d89f18428973ea8539398f714139db66f196188d","source":{"kind":"arxiv","id":"2602.20266","version":2},"attestation_state":"computed","paper":{"title":"Multiple Poisson-Dirichlet diffusions on generalized Kingman simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","q-bio.PE","stat.TH"],"primary_cat":"math.PR","authors_text":"Cristina Costantini, Matteo Ruggiero","submitted_at":"2026-02-23T19:00:15Z","abstract_excerpt":"We construct a new class of infinite-dimensional diffusions with values in a generalized Kingman simplex with finitely many marks. The model describes the temporal evolution of the relative frequencies of infinitely many types that are labeled by a finite number $H$ of marks, but unlabeled within each mark. We first establish a blockwise skew-product representation for a finite-type Wright-Fisher diffusion, extending the aggregation-renormalization self-similarity property of Dirichlet laws. The decomposition separates an $H$-dimensional Wright-Fisher diffusion governing the evolving random ma"},"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":"2602.20266","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-02-23T19:00:15Z","cross_cats_sorted":["math.ST","q-bio.PE","stat.TH"],"title_canon_sha256":"2c180cbe336bfa7ca2f33ae0e77f345abb0238bc47be60eb6e9a5cffa8731379","abstract_canon_sha256":"8e1d573d4bcba6ceee05394997350d028bafdf5a34717ef612e2c9081a9c576f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:31.257291Z","signature_b64":"+AeXocI/SMswWvfryz0i+qpYDibMsOM7cfHK3udyT5bq5DHkLyefg/YfAWxS/mmBl6lSHnaVwNfJp9QBXLADAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbb04be057b2685cd16588e2d89f18428973ea8539398f714139db66f196188d","last_reissued_at":"2026-06-11T01:09:31.256156Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:31.256156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple Poisson-Dirichlet diffusions on generalized Kingman simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","q-bio.PE","stat.TH"],"primary_cat":"math.PR","authors_text":"Cristina Costantini, Matteo Ruggiero","submitted_at":"2026-02-23T19:00:15Z","abstract_excerpt":"We construct a new class of infinite-dimensional diffusions with values in a generalized Kingman simplex with finitely many marks. The model describes the temporal evolution of the relative frequencies of infinitely many types that are labeled by a finite number $H$ of marks, but unlabeled within each mark. We first establish a blockwise skew-product representation for a finite-type Wright-Fisher diffusion, extending the aggregation-renormalization self-similarity property of Dirichlet laws. The decomposition separates an $H$-dimensional Wright-Fisher diffusion governing the evolving random ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.20266","kind":"arxiv","version":2},"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/2602.20266/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":"2602.20266","created_at":"2026-06-11T01:09:31.256313+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.20266v2","created_at":"2026-06-11T01:09:31.256313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.20266","created_at":"2026-06-11T01:09:31.256313+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOYEXYCXWJUF","created_at":"2026-06-11T01:09:31.256313+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOYEXYCXWJUFZULF","created_at":"2026-06-11T01:09:31.256313+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOYEXYCX","created_at":"2026-06-11T01:09:31.256313+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK","json":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK.json","graph_json":"https://pith.science/api/pith-number/ZOYEXYCXWJUFZULFRDRNRHYYIK/graph.json","events_json":"https://pith.science/api/pith-number/ZOYEXYCXWJUFZULFRDRNRHYYIK/events.json","paper":"https://pith.science/paper/ZOYEXYCX"},"agent_actions":{"view_html":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK","download_json":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK.json","view_paper":"https://pith.science/paper/ZOYEXYCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.20266&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOYEXYCXWJUFZULFRDRNRHYYIK/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOYEXYCXWJUFZULFRDRNRHYYIK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK/action/storage_attestation","attest_author":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK/action/author_attestation","sign_citation":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK/action/citation_signature","submit_replication":"https://pith.science/pith/ZOYEXYCXWJUFZULFRDRNRHYYIK/action/replication_record"}},"created_at":"2026-06-11T01:09:31.256313+00:00","updated_at":"2026-06-11T01:09:31.256313+00:00"}