{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FNQAUEJE34SWT7D4662YR7LBIX","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":"4cbd0be558bf28dc95a39188c2ec3a7231d158fbc9c27a0dac01742b24144374","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-20T13:39:16Z","title_canon_sha256":"e6dcf2b3d5c9bb29203a0b7be5d3c4f99cecf0e85fad6f8e2c41a66cb3405a5d"},"schema_version":"1.0","source":{"id":"1704.06138","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06138","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06138v2","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06138","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"FNQAUEJE34SW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FNQAUEJE34SWT7D4","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FNQAUEJE","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:52e934f5583ab0f867c4b31fd48ef8932d316114047560df28b8a91507393214","target":"graph","created_at":"2026-05-18T00:35:55Z","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":"Sets of invariant measures are considered for continuous maps of a metric compact set. We take Kantorovich metric to calculate distance between measures and Hausdorff metrics to calculate distance between compact sets. Consider the function that makes correspondence between a continuous map and the set of all its Borel probability invariant measures. We demonstrate that a typical map is a continuity point of that function. Using approaches of Takens' tolerance stability theory we provide some corollaries that demonstrate that for a typical map points are structurally stable in a statistical se","authors_text":"Sergey Kryzhevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-20T13:39:16Z","title":"Sets of invariant measures and Cesaro stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06138","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":"sha256:0b4d22511f0611789885bcbd27c2256e8f60ff7269fd9e9675eefd365bc1faa5","target":"record","created_at":"2026-05-18T00:35:55Z","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":"4cbd0be558bf28dc95a39188c2ec3a7231d158fbc9c27a0dac01742b24144374","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-20T13:39:16Z","title_canon_sha256":"e6dcf2b3d5c9bb29203a0b7be5d3c4f99cecf0e85fad6f8e2c41a66cb3405a5d"},"schema_version":"1.0","source":{"id":"1704.06138","kind":"arxiv","version":2}},"canonical_sha256":"2b600a1124df2569fc7cf7b588fd6145ecc54affe842119df6f6b0ec4cf16011","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b600a1124df2569fc7cf7b588fd6145ecc54affe842119df6f6b0ec4cf16011","first_computed_at":"2026-05-18T00:35:55.241340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.241340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IkfcM96hJxWLAmH0+Uwr3UISXS/D6g6qPnvdatUPvjQMxTmp6RepQ3j4IPJZftVd5SvLwExDKGax0r3R/6+OCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.241738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06138","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b4d22511f0611789885bcbd27c2256e8f60ff7269fd9e9675eefd365bc1faa5","sha256:52e934f5583ab0f867c4b31fd48ef8932d316114047560df28b8a91507393214"],"state_sha256":"7b43bf8436b1c854b45825976d21919504b944bba80a1887bc2fb954d072b0fb"}