{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AEWWHER3L7C5T4IBAILSEYHFY2","short_pith_number":"pith:AEWWHER3","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"},"canonical_sha256":"012d63923b5fc5d9f10102172260e5c69be99a9a0abe6ba1d2d682d8bc2db67f","source":{"kind":"arxiv","id":"1506.01495","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01495","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01495v1","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01495","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"AEWWHER3L7C5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AEWWHER3L7C5T4IB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AEWWHER3","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AEWWHER3L7C5T4IBAILSEYHFY2","target":"record","payload":{"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"},"canonical_sha256":"012d63923b5fc5d9f10102172260e5c69be99a9a0abe6ba1d2d682d8bc2db67f","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"},"source_kind":"arxiv","source_id":"1506.01495","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jza8MqSbgNKt7i12uhtTFR5Nvd/0EDHnu/SaJCnStjxNzc4D5luFJLhWByDm3RbkoBHgqGEwcB3VMiB7rw1SDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:26:45.798649Z"},"content_sha256":"6fe1aa0dc5b7817754c4c9744a466dc74699187dade7158c8b43199895f26db9","schema_version":"1.0","event_id":"sha256:6fe1aa0dc5b7817754c4c9744a466dc74699187dade7158c8b43199895f26db9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AEWWHER3L7C5T4IBAILSEYHFY2","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:57:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D309Zy8UXJ793+Nw7b28fCsAfN7W7x9plnkHMojLxGP2D4WRPoO2VkzX76dqFFbpZ0tiuz5rqkohQTdDK8oQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:26:45.799275Z"},"content_sha256":"a54f890f06a27baf94f506693c4e4eb7d9be8e3c12a10326e6deeb022fa6ccbe","schema_version":"1.0","event_id":"sha256:a54f890f06a27baf94f506693c4e4eb7d9be8e3c12a10326e6deeb022fa6ccbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/bundle.json","state_url":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AEWWHER3L7C5T4IBAILSEYHFY2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T04:26:45Z","links":{"resolver":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2","bundle":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/bundle.json","state":"https://pith.science/pith/AEWWHER3L7C5T4IBAILSEYHFY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AEWWHER3L7C5T4IBAILSEYHFY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AEWWHER3L7C5T4IBAILSEYHFY2","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":"d31f77ac9462a004d952f0a2517795e4cbcd7509fb665016f59ff31caa06d1b1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:48:41Z","title_canon_sha256":"305edc16868b893896e90cd70cbf6477acd3910a136f2e08358d2ddfd312d21f"},"schema_version":"1.0","source":{"id":"1506.01495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01495","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01495v1","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01495","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"AEWWHER3L7C5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AEWWHER3L7C5T4IB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AEWWHER3","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:a54f890f06a27baf94f506693c4e4eb7d9be8e3c12a10326e6deeb022fa6ccbe","target":"graph","created_at":"2026-05-18T01:57:41Z","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"},"paper":{"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.","authors_text":"Harry Crane","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:48:41Z","title":"Lipschitz partition processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01495","kind":"arxiv","version":1},"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":"sha256:6fe1aa0dc5b7817754c4c9744a466dc74699187dade7158c8b43199895f26db9","target":"record","created_at":"2026-05-18T01:57:41Z","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":"d31f77ac9462a004d952f0a2517795e4cbcd7509fb665016f59ff31caa06d1b1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:48:41Z","title_canon_sha256":"305edc16868b893896e90cd70cbf6477acd3910a136f2e08358d2ddfd312d21f"},"schema_version":"1.0","source":{"id":"1506.01495","kind":"arxiv","version":1}},"canonical_sha256":"012d63923b5fc5d9f10102172260e5c69be99a9a0abe6ba1d2d682d8bc2db67f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"012d63923b5fc5d9f10102172260e5c69be99a9a0abe6ba1d2d682d8bc2db67f","first_computed_at":"2026-05-18T01:57:41.278416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:41.278416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/5iS7OFFtctHY4tADiLj+vMTj0a+XkgHJ9mmtH0WWSBjVPfBLC1vM18LxOIsnuTDEG8F4UfyQbCek+JSL/FMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:41.279185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe1aa0dc5b7817754c4c9744a466dc74699187dade7158c8b43199895f26db9","sha256:a54f890f06a27baf94f506693c4e4eb7d9be8e3c12a10326e6deeb022fa6ccbe"],"state_sha256":"137214f6c1cff9d99cc0c4a7f99eeab38ed1c5d7b7bbb86ee8a75308e9fe5f27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EZ9dXgiwQCnpCVyvmdC6urdZOz2CBb9zv4eshZUbuZTD+VabWF7DlQSfB2cC5GrKQoQm5am4gqfTO9TXFoPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T04:26:45.802777Z","bundle_sha256":"41d903743ad1ae41e8799b7a055955dc65fbd14594e6ad87bdee15e21a61802f"}}