{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T6BPHPHHHNW7CAQIFUTRIZVLHL","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":"f3200c0859892ddf5b320f03f6bbb74ff7486e8e2948d5d4c1a1bbc85fcd8ac1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-05T17:12:49Z","title_canon_sha256":"7d6825686ec8c2f83a5aa1aef945bf9e09c8657124825fd642471853b602eb0d"},"schema_version":"1.0","source":{"id":"1707.01472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01472","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01472v1","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01472","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"T6BPHPHHHNW7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T6BPHPHHHNW7CAQI","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T6BPHPHH","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:da5859675c2d8c73c7c8ffc30f5d1a6837c64f1fbaa1839fb485380f65cc6062","target":"graph","created_at":"2026-05-18T00:22:20Z","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":"We define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability. We prove that an invariant measure of a continuous system is empirically stochastically stable if and only if it is physical. We also define the empiric stochastic stability of a weak*-compact set of invariant measures instead of a single measure. Even when the system has not physical measures it still has minimal empirically stochastically stable sets of measures. We prove that such sets are necessarily composed by pseudo-physical measures. Finally,","authors_text":"Eleonora Catsigeras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-05T17:12:49Z","title":"Empiric stochastic stability of physical and pseudo-physical measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01472","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:ada483c6f0a623a03706974c0d5d50eb36706746943b0b24fa512ba6b7caf344","target":"record","created_at":"2026-05-18T00:22:20Z","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":"f3200c0859892ddf5b320f03f6bbb74ff7486e8e2948d5d4c1a1bbc85fcd8ac1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-05T17:12:49Z","title_canon_sha256":"7d6825686ec8c2f83a5aa1aef945bf9e09c8657124825fd642471853b602eb0d"},"schema_version":"1.0","source":{"id":"1707.01472","kind":"arxiv","version":1}},"canonical_sha256":"9f82f3bce73b6df102082d271466ab3affcb2c1a137625f3886204359f5aa349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f82f3bce73b6df102082d271466ab3affcb2c1a137625f3886204359f5aa349","first_computed_at":"2026-05-18T00:22:20.893696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:20.893696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dyh6TAb4SQxxuNzjrIczQv4+uJWWl7Xps0mlCpiNmFkvwPjnTPHwyvdr3U2sXrPDn4y/yrIuvIO07hPMplDeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:20.894261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ada483c6f0a623a03706974c0d5d50eb36706746943b0b24fa512ba6b7caf344","sha256:da5859675c2d8c73c7c8ffc30f5d1a6837c64f1fbaa1839fb485380f65cc6062"],"state_sha256":"248040ca55bea23a49a49c22fedab48badcaa94c9ee93580e5c989a2d74ce8a4"}