{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AEWWHER3L7C5T4IBAILSEYHFY2","short_pith_number":"pith:AEWWHER3","schema_version":"1.0","canonical_sha256":"012d63923b5fc5d9f10102172260e5c69be99a9a0abe6ba1d2d682d8bc2db67f","source":{"kind":"arxiv","id":"1506.01495","version":1},"attestation_state":"computed","paper":{"title":"Lipschitz partition processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Harry Crane","submitted_at":"2015-06-04T07:48:41Z","abstract_excerpt":"We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps on partitions. By this construction, the Markovian consistency property is readily satisfied; that is, the finite restrictions of any Lipschitz partition process comprise a compatible collection of finite state space Markov chains. We further characterize the class of exchangeable Lipschitz partition processes by a novel set-valued matrix operation."},"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":"1506.01495","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:48:41Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"305edc16868b893896e90cd70cbf6477acd3910a136f2e08358d2ddfd312d21f","abstract_canon_sha256":"d31f77ac9462a004d952f0a2517795e4cbcd7509fb665016f59ff31caa06d1b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:41.279185Z","signature_b64":"/5iS7OFFtctHY4tADiLj+vMTj0a+XkgHJ9mmtH0WWSBjVPfBLC1vM18LxOIsnuTDEG8F4UfyQbCek+JSL/FMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"012d63923b5fc5d9f10102172260e5c69be99a9a0abe6ba1d2d682d8bc2db67f","last_reissued_at":"2026-05-18T01:57:41.278416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:41.278416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz partition processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Harry Crane","submitted_at":"2015-06-04T07:48:41Z","abstract_excerpt":"We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps on partitions. By this construction, the Markovian consistency property is readily satisfied; that is, the finite restrictions of any Lipschitz partition process comprise a compatible collection of finite state space Markov chains. We further characterize the class of exchangeable Lipschitz partition processes by a novel set-valued matrix operation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01495","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":""},"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":"1506.01495","created_at":"2026-05-18T01:57:41.278543+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01495v1","created_at":"2026-05-18T01:57:41.278543+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01495","created_at":"2026-05-18T01:57:41.278543+00:00"},{"alias_kind":"pith_short_12","alias_value":"AEWWHER3L7C5","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AEWWHER3L7C5T4IB","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AEWWHER3","created_at":"2026-05-18T12:29:10.953037+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/AEWWHER3L7C5T4IBAILSEYHFY2","json":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2.json","graph_json":"https://pith.science/api/pith-number/AEWWHER3L7C5T4IBAILSEYHFY2/graph.json","events_json":"https://pith.science/api/pith-number/AEWWHER3L7C5T4IBAILSEYHFY2/events.json","paper":"https://pith.science/paper/AEWWHER3"},"agent_actions":{"view_html":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2","download_json":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2.json","view_paper":"https://pith.science/paper/AEWWHER3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01495&json=true","fetch_graph":"https://pith.science/api/pith-number/AEWWHER3L7C5T4IBAILSEYHFY2/graph.json","fetch_events":"https://pith.science/api/pith-number/AEWWHER3L7C5T4IBAILSEYHFY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/action/storage_attestation","attest_author":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/action/author_attestation","sign_citation":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/action/citation_signature","submit_replication":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/action/replication_record"}},"created_at":"2026-05-18T01:57:41.278543+00:00","updated_at":"2026-05-18T01:57:41.278543+00:00"}