{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NNM3WWC3SW4KNQE25YUGXKZZKH","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":"c80dff53489e6cf7b1e095e5c799bf1edd33b1777d32647df440be9ea0578f83","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-21T15:07:13Z","title_canon_sha256":"a250d3f698693123144096be1e6c6a3baf0a129fab9a077aa867cd63395f1127"},"schema_version":"1.0","source":{"id":"1508.05299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05299","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05299v2","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05299","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"NNM3WWC3SW4K","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNM3WWC3SW4KNQE2","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNM3WWC3","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:856ba13d912b03cb0cc67015a5a0258c781ecc3bb4ae07459c8d90e6746d72ab","target":"graph","created_at":"2026-05-18T01:20:55Z","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":"Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \\textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as the noise fades away. Chemists, economists, and computer scientists have been studying irreducible perturbations built with exponential maps. Under these assumptions, Young proved the existence of and computed the stable states in cubic time. We fully drop these assumptions, generalize Young's technique, and show that stability is decidable as long as $f\\in ","authors_text":"Stephane Le Roux, Volker Betz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-21T15:07:13Z","title":"Stable states of perturbed Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05299","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":"sha256:5cb3ce243357ab321de765670e2c14afbc45a6d69835ddbba7765146697e88c6","target":"record","created_at":"2026-05-18T01:20:55Z","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":"c80dff53489e6cf7b1e095e5c799bf1edd33b1777d32647df440be9ea0578f83","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-21T15:07:13Z","title_canon_sha256":"a250d3f698693123144096be1e6c6a3baf0a129fab9a077aa867cd63395f1127"},"schema_version":"1.0","source":{"id":"1508.05299","kind":"arxiv","version":2}},"canonical_sha256":"6b59bb585b95b8a6c09aee286bab3951d04f10629ea322b5db8599ae6b5968ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b59bb585b95b8a6c09aee286bab3951d04f10629ea322b5db8599ae6b5968ad","first_computed_at":"2026-05-18T01:20:55.853751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:55.853751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+QDhfXmh2FirUw60er7P1qRSXIshP9J7B4ubVOu5agMneb+TKieUI8SGNvAA0DJFZMzudVDxrB7+70nmduESCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:55.854284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cb3ce243357ab321de765670e2c14afbc45a6d69835ddbba7765146697e88c6","sha256:856ba13d912b03cb0cc67015a5a0258c781ecc3bb4ae07459c8d90e6746d72ab"],"state_sha256":"e288513636cb0b646c73c848e84e18e5e74d6d33eae004fcb3d87cfd790d3417"}