{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DZ77FY5ECUABFMNDGFZBXRGFR6","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":"5c50d6135a10ae4f3ae7555770780bdf2deec25f327482b50f24a6e4c0232a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-25T13:34:46Z","title_canon_sha256":"c11a859c266096a75d875106ddfedcb8aa025908575d98b4e089b04dbd43cef9"},"schema_version":"1.0","source":{"id":"1907.11036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11036","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11036v1","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11036","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"DZ77FY5ECUAB","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DZ77FY5ECUABFMND","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DZ77FY5E","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:55161a5d68a9cc6199768c7af19f8201469185306d5d99e9a91e69b846f1e151","target":"graph","created_at":"2026-05-17T23:39:33Z","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":"In this paper, we show that the Ricci curvature lower bound in Ollivier's Wasserstein metric sense of a continuous time jumping Markov process on a graph can be characterized by some optimal coupling generator and provide the construction of this latter. Some previous results of Ollivier for discrete time Markov chains are generalized to the actual continuous time case. We propose a comparison technique with some death-birth process on $\\mathbb N$ to obtain some explicit exponential convergence rate, by modifying the metric. A counterpart of Zhong-Yang's estimate is established in the case whe","authors_text":"Liming Wu, Lingyan Cheng, Ruinan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-25T13:34:46Z","title":"Ricci curvature and $W_1$-exponential convergence of Markov processes on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11036","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:eb60c3ddc7fc4c6b1be34483d71f61d7aa7c25431520c170ec57d96457273c34","target":"record","created_at":"2026-05-17T23:39:33Z","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":"5c50d6135a10ae4f3ae7555770780bdf2deec25f327482b50f24a6e4c0232a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-25T13:34:46Z","title_canon_sha256":"c11a859c266096a75d875106ddfedcb8aa025908575d98b4e089b04dbd43cef9"},"schema_version":"1.0","source":{"id":"1907.11036","kind":"arxiv","version":1}},"canonical_sha256":"1e7ff2e3a4150012b1a331721bc4c58fb454a13d1d921f6c948bfce7c9a82582","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e7ff2e3a4150012b1a331721bc4c58fb454a13d1d921f6c948bfce7c9a82582","first_computed_at":"2026-05-17T23:39:33.678766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:33.678766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RzGVbLtJh5YtkmRxYUbBxMXw808G45Zrv/cUNTSvfMBb4i+kCjyfbfF66r93JTJnHQJNHAJcmr1eZM6YZJumAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:33.679403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb60c3ddc7fc4c6b1be34483d71f61d7aa7c25431520c170ec57d96457273c34","sha256:55161a5d68a9cc6199768c7af19f8201469185306d5d99e9a91e69b846f1e151"],"state_sha256":"8e0fc17880d329ee622390ad5b50bf0f2cca86ea709b954d6b8ac4c22a23c501"}