{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NGIHI2ORESPW6UZ6ZGKTNEDFST","short_pith_number":"pith:NGIHI2OR","schema_version":"1.0","canonical_sha256":"69907469d1249f6f533ec99536906594c766879c246f0860c9850a7f037de903","source":{"kind":"arxiv","id":"2402.12257","version":1},"attestation_state":"computed","paper":{"title":"Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.DS","authors_text":"Horia Cornean, \\\"Ozkan Karabacak, Rafael Wisniewski","submitted_at":"2024-02-19T16:14:35Z","abstract_excerpt":"Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant function (counterpart of the Lyapunov density in deterministic systems) implies sweeping of a Markov process out of the sets where this function is integrable. Such a function can be used as a certificate of convergence in probability of a stochastic system. We apply this technique to Markov processes induced by a quantum system with non-demolition measurement "},"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":"2402.12257","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-02-19T16:14:35Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"ac99c1306ac83885d320e69c438dc1e8d65279e81495d9dd50e351b91c53b071","abstract_canon_sha256":"08915216fd61a42bb7de3a48edce3210b030f31a1dd03075e2db6adeeafd65ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:46:51.130484Z","signature_b64":"KHw3EeHAWMYk8g8HgF6dNNSJHW4nTZcz/akpv/JewNnPOjnT5GhVLdTVIcPNezl7ichf6ZDxQ1u6A5lpuDcBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69907469d1249f6f533ec99536906594c766879c246f0860c9850a7f037de903","last_reissued_at":"2026-07-05T07:46:51.130111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:46:51.130111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lyapunov Densities For Markov Processes: An Application To Quantum Systems With Non-Demolition Measurements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.DS","authors_text":"Horia Cornean, \\\"Ozkan Karabacak, Rafael Wisniewski","submitted_at":"2024-02-19T16:14:35Z","abstract_excerpt":"Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant function (counterpart of the Lyapunov density in deterministic systems) implies sweeping of a Markov process out of the sets where this function is integrable. Such a function can be used as a certificate of convergence in probability of a stochastic system. We apply this technique to Markov processes induced by a quantum system with non-demolition measurement "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.12257","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.12257/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2402.12257","created_at":"2026-07-05T07:46:51.130165+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.12257v1","created_at":"2026-07-05T07:46:51.130165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.12257","created_at":"2026-07-05T07:46:51.130165+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGIHI2ORESPW","created_at":"2026-07-05T07:46:51.130165+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGIHI2ORESPW6UZ6","created_at":"2026-07-05T07:46:51.130165+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGIHI2OR","created_at":"2026-07-05T07:46:51.130165+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/NGIHI2ORESPW6UZ6ZGKTNEDFST","json":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST.json","graph_json":"https://pith.science/api/pith-number/NGIHI2ORESPW6UZ6ZGKTNEDFST/graph.json","events_json":"https://pith.science/api/pith-number/NGIHI2ORESPW6UZ6ZGKTNEDFST/events.json","paper":"https://pith.science/paper/NGIHI2OR"},"agent_actions":{"view_html":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST","download_json":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST.json","view_paper":"https://pith.science/paper/NGIHI2OR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.12257&json=true","fetch_graph":"https://pith.science/api/pith-number/NGIHI2ORESPW6UZ6ZGKTNEDFST/graph.json","fetch_events":"https://pith.science/api/pith-number/NGIHI2ORESPW6UZ6ZGKTNEDFST/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST/action/storage_attestation","attest_author":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST/action/author_attestation","sign_citation":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST/action/citation_signature","submit_replication":"https://pith.science/pith/NGIHI2ORESPW6UZ6ZGKTNEDFST/action/replication_record"}},"created_at":"2026-07-05T07:46:51.130165+00:00","updated_at":"2026-07-05T07:46:51.130165+00:00"}