{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:PHLE5NBAQHYL5WEQYV4LU4A2IH","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":"0cffc14968f0eb50b31933ef77d4aa0dc1e5c9b00e42867c9ff1868673257cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-11-04T03:42:55Z","title_canon_sha256":"ab9295939be5413ea1432e23dee9a845eff608c8e0dad56b19f8323a89e19c1b"},"schema_version":"1.0","source":{"id":"0711.0493","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0493","created_at":"2026-07-04T15:15:11Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0493v2","created_at":"2026-07-04T15:15:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0493","created_at":"2026-07-04T15:15:11Z"},{"alias_kind":"pith_short_12","alias_value":"PHLE5NBAQHYL","created_at":"2026-07-04T15:15:11Z"},{"alias_kind":"pith_short_16","alias_value":"PHLE5NBAQHYL5WEQ","created_at":"2026-07-04T15:15:11Z"},{"alias_kind":"pith_short_8","alias_value":"PHLE5NBA","created_at":"2026-07-04T15:15:11Z"}],"graph_snapshots":[{"event_id":"sha256:c71be06c3563e766e8ca40aa1f4fa82aa0c64bb0b54572d01d80a96dfebb4753","target":"graph","created_at":"2026-07-04T15:15:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0711.0493/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.","authors_text":"David White, Krzysztof Burdzy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-11-04T03:42:55Z","title":"Markov processes with product-form stationary distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0493","kind":"arxiv","version":2},"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:a6b3f9014e86d5c6ed01c375a8dcb9d4b231345b4d68266b949a9730e1662311","target":"record","created_at":"2026-07-04T15:15:11Z","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":"0cffc14968f0eb50b31933ef77d4aa0dc1e5c9b00e42867c9ff1868673257cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-11-04T03:42:55Z","title_canon_sha256":"ab9295939be5413ea1432e23dee9a845eff608c8e0dad56b19f8323a89e19c1b"},"schema_version":"1.0","source":{"id":"0711.0493","kind":"arxiv","version":2}},"canonical_sha256":"79d64eb42081f0bed890c578ba701a41e78a75f00087b7a1b7df81c39c7da3fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79d64eb42081f0bed890c578ba701a41e78a75f00087b7a1b7df81c39c7da3fc","first_computed_at":"2026-07-04T15:15:11.727806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:15:11.727806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5QTVSMmEzmBUIEibQI3Y+8H1p+wUjukb8WEVZ6QMzDTLloW7HaSdMIta5MQ45iD3xfWLj4CqqMsVnQuPOttnBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:15:11.728248Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.0493","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6b3f9014e86d5c6ed01c375a8dcb9d4b231345b4d68266b949a9730e1662311","sha256:c71be06c3563e766e8ca40aa1f4fa82aa0c64bb0b54572d01d80a96dfebb4753"],"state_sha256":"164cac0fa58c7da4ba072de66d430132bf3b863b80072e112826fd92c0f40501"}