{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SLTDXKD3UJ5OWZNHZQJO35K3M6","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":"97b664a1858afc2e303d56d2a6ee5e6dc77bd88da28e9c2c9fc1c3ef2101e221","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-26T02:43:50Z","title_canon_sha256":"b88ba3469e18b4265155b7ede5facc3b77b322c7d24a18145b9a8c17c2e97180"},"schema_version":"1.0","source":{"id":"2412.19029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19029","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19029v1","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19029","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"SLTDXKD3UJ5O","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_16","alias_value":"SLTDXKD3UJ5OWZNH","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_8","alias_value":"SLTDXKD3","created_at":"2026-07-05T09:54:15Z"}],"graph_snapshots":[{"event_id":"sha256:e210307c739d54a0ff196d13e236fcb5ede4eb04d59855bd06484e9e1898e941","target":"graph","created_at":"2026-07-05T09:54:15Z","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/2412.19029/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the ergodicity of Markov--Feller semigroups on Polish spaces, focusing on very weak regularity conditions, particularly the Ces\\`aro eventual continuity. First, it is showed that the Ces\\`aro average of such semigroups weakly converges to an ergodic measure when starting from its support. This leads to a characterization of the relationship between Ces\\`aro eventual continuity, Ces\\`aro e-property, and weak-* mean ergodicity. Next, serval criteria are provided for the existence and uniqueness of invariant measures via Ces\\`aro eventual continuity and lower bound conditi","authors_text":"Fuzhou Gong, Yong Liu, Yuan Liu, Ziyu Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-26T02:43:50Z","title":"Ergodicity for eventually continuous Markov--Feller semigroups on Polish spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19029","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":"sha256:608d7872f5342c3c9497cc91c0ce5a5e8dd9d082bf1cd7e50783da2d479762d2","target":"record","created_at":"2026-07-05T09:54:15Z","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":"97b664a1858afc2e303d56d2a6ee5e6dc77bd88da28e9c2c9fc1c3ef2101e221","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-26T02:43:50Z","title_canon_sha256":"b88ba3469e18b4265155b7ede5facc3b77b322c7d24a18145b9a8c17c2e97180"},"schema_version":"1.0","source":{"id":"2412.19029","kind":"arxiv","version":1}},"canonical_sha256":"92e63ba87ba27aeb65a7cc12edf55b679ec6c1dd62aec973d3824fc28bc6bf72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92e63ba87ba27aeb65a7cc12edf55b679ec6c1dd62aec973d3824fc28bc6bf72","first_computed_at":"2026-07-05T09:54:15.107081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:15.107081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eh2dVxEIRJTRfTT8saReZZGRBklSrXCq0j7GNaSmo3+lDJmXx9oHv9PKmW1OfUhiktWc2X/LuuXhKmDQ41GdBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:15.107570Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:608d7872f5342c3c9497cc91c0ce5a5e8dd9d082bf1cd7e50783da2d479762d2","sha256:e210307c739d54a0ff196d13e236fcb5ede4eb04d59855bd06484e9e1898e941"],"state_sha256":"bbd5e15a9e698b61400ff20c5f3963ec037a70c3a30b61f657315a1f43da955e"}