{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T6BPHPHHHNW7CAQIFUTRIZVLHL","short_pith_number":"pith:T6BPHPHH","schema_version":"1.0","canonical_sha256":"9f82f3bce73b6df102082d271466ab3affcb2c1a137625f3886204359f5aa349","source":{"kind":"arxiv","id":"1707.01472","version":1},"attestation_state":"computed","paper":{"title":"Empiric stochastic stability of physical and pseudo-physical measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras","submitted_at":"2017-07-05T17:12:49Z","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,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.01472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-05T17:12:49Z","cross_cats_sorted":[],"title_canon_sha256":"7d6825686ec8c2f83a5aa1aef945bf9e09c8657124825fd642471853b602eb0d","abstract_canon_sha256":"f3200c0859892ddf5b320f03f6bbb74ff7486e8e2948d5d4c1a1bbc85fcd8ac1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:20.894261Z","signature_b64":"dyh6TAb4SQxxuNzjrIczQv4+uJWWl7Xps0mlCpiNmFkvwPjnTPHwyvdr3U2sXrPDn4y/yrIuvIO07hPMplDeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f82f3bce73b6df102082d271466ab3affcb2c1a137625f3886204359f5aa349","last_reissued_at":"2026-05-18T00:22:20.893696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:20.893696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Empiric stochastic stability of physical and pseudo-physical measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eleonora Catsigeras","submitted_at":"2017-07-05T17:12:49Z","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,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01472","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.01472","created_at":"2026-05-18T00:22:20.893784+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01472v1","created_at":"2026-05-18T00:22:20.893784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01472","created_at":"2026-05-18T00:22:20.893784+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6BPHPHHHNW7","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6BPHPHHHNW7CAQI","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6BPHPHH","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL","json":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL.json","graph_json":"https://pith.science/api/pith-number/T6BPHPHHHNW7CAQIFUTRIZVLHL/graph.json","events_json":"https://pith.science/api/pith-number/T6BPHPHHHNW7CAQIFUTRIZVLHL/events.json","paper":"https://pith.science/paper/T6BPHPHH"},"agent_actions":{"view_html":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL","download_json":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL.json","view_paper":"https://pith.science/paper/T6BPHPHH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01472&json=true","fetch_graph":"https://pith.science/api/pith-number/T6BPHPHHHNW7CAQIFUTRIZVLHL/graph.json","fetch_events":"https://pith.science/api/pith-number/T6BPHPHHHNW7CAQIFUTRIZVLHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL/action/storage_attestation","attest_author":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL/action/author_attestation","sign_citation":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL/action/citation_signature","submit_replication":"https://pith.science/pith/T6BPHPHHHNW7CAQIFUTRIZVLHL/action/replication_record"}},"created_at":"2026-05-18T00:22:20.893784+00:00","updated_at":"2026-05-18T00:22:20.893784+00:00"}