{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5AGUOLFO5MWIGZ27W5JH6NP2EE","short_pith_number":"pith:5AGUOLFO","schema_version":"1.0","canonical_sha256":"e80d472caeeb2c83675fb7527f35fa2136b925423ce7f4f7217418304c236ea9","source":{"kind":"arxiv","id":"1307.1713","version":2},"attestation_state":"computed","paper":{"title":"Exchangeable Markov Processes on $[k]^{\\zz{N}}$ with Cadlag Sample Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harry Crane, Steven P. Lalley","submitted_at":"2013-07-05T20:21:04Z","abstract_excerpt":"Any exchangeable Markov processes on $[k]^{\\mathbb{N}}$ with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded variation. Furthermore, any such process has a de Finetti-type description as a mixture of i.i.d. copies of time-inhomogeneous Markov processes on $[k]$. In the Feller case, these time-inhomogeneous Markov processes have a relatively simple structure; however, in the non-Feller case a greater variety of behaviors is possible since the transition law of the underlying Markov process on $[k]^{\\zz{N}}$ can depend in a non"},"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":"1307.1713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-05T20:21:04Z","cross_cats_sorted":[],"title_canon_sha256":"e0911ce1a80e78b0b6ad8f726b008b8d52d26910fab41be82347989756f3b8e4","abstract_canon_sha256":"84863982e86a8b99e8ce02b548e2841802c42d3ecba218cbf853fc8f4620055e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:34.338892Z","signature_b64":"P2eOeK9iEf/ongw8EzP/NY4Alqsuao5/jNi/BfDcXCu+08AQx6to4nyG8vO9Q7vl+7vmvrh01HNjkQ4O4VayDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e80d472caeeb2c83675fb7527f35fa2136b925423ce7f4f7217418304c236ea9","last_reissued_at":"2026-05-18T03:06:34.338436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:34.338436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exchangeable Markov Processes on $[k]^{\\zz{N}}$ with Cadlag Sample Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harry Crane, Steven P. Lalley","submitted_at":"2013-07-05T20:21:04Z","abstract_excerpt":"Any exchangeable Markov processes on $[k]^{\\mathbb{N}}$ with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded variation. Furthermore, any such process has a de Finetti-type description as a mixture of i.i.d. copies of time-inhomogeneous Markov processes on $[k]$. In the Feller case, these time-inhomogeneous Markov processes have a relatively simple structure; however, in the non-Feller case a greater variety of behaviors is possible since the transition law of the underlying Markov process on $[k]^{\\zz{N}}$ can depend in a non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1713","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":""},"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":"1307.1713","created_at":"2026-05-18T03:06:34.338503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.1713v2","created_at":"2026-05-18T03:06:34.338503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1713","created_at":"2026-05-18T03:06:34.338503+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AGUOLFO5MWI","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AGUOLFO5MWIGZ27","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AGUOLFO","created_at":"2026-05-18T12:27:34.582898+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/5AGUOLFO5MWIGZ27W5JH6NP2EE","json":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE.json","graph_json":"https://pith.science/api/pith-number/5AGUOLFO5MWIGZ27W5JH6NP2EE/graph.json","events_json":"https://pith.science/api/pith-number/5AGUOLFO5MWIGZ27W5JH6NP2EE/events.json","paper":"https://pith.science/paper/5AGUOLFO"},"agent_actions":{"view_html":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE","download_json":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE.json","view_paper":"https://pith.science/paper/5AGUOLFO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.1713&json=true","fetch_graph":"https://pith.science/api/pith-number/5AGUOLFO5MWIGZ27W5JH6NP2EE/graph.json","fetch_events":"https://pith.science/api/pith-number/5AGUOLFO5MWIGZ27W5JH6NP2EE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE/action/storage_attestation","attest_author":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE/action/author_attestation","sign_citation":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE/action/citation_signature","submit_replication":"https://pith.science/pith/5AGUOLFO5MWIGZ27W5JH6NP2EE/action/replication_record"}},"created_at":"2026-05-18T03:06:34.338503+00:00","updated_at":"2026-05-18T03:06:34.338503+00:00"}