{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:IOTQFLHWK23YMUVV2S2UUML35N","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":"2e774a1f558e91e90ad249535f497302a1c104d388e0eafe84e9192d686fafff","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-10-22T21:15:54Z","title_canon_sha256":"f2f1958c9eb6549a2abf6bb5b5031cd85c9c847e6c79ca0b3be0e4a9507a7487"},"schema_version":"1.0","source":{"id":"math-ph/0610054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0610054","created_at":"2026-07-04T15:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0610054v2","created_at":"2026-07-04T15:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0610054","created_at":"2026-07-04T15:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"IOTQFLHWK23Y","created_at":"2026-07-04T15:02:21Z"},{"alias_kind":"pith_short_16","alias_value":"IOTQFLHWK23YMUVV","created_at":"2026-07-04T15:02:21Z"},{"alias_kind":"pith_short_8","alias_value":"IOTQFLHW","created_at":"2026-07-04T15:02:21Z"}],"graph_snapshots":[{"event_id":"sha256:a6d1f816ee967b21e03a5470465ce7aa66a9de4f26414efc8a3b6ebcfe5899ba","target":"graph","created_at":"2026-07-04T15:02:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0610054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the weak coupling limit for a quantum system consisting of a small subsystem and reservoirs. It is known rigorously since [Dav74] that the Heisenberg evolution restricted to the small system converges in an appropriate sense to a Markovian semigroup. In the nineties, Accardi, Frigerio and Lu [AFL90] initiated an investigation of the convergence of the unreduced unitary evolution to a singular unitary evolution generated by a quantum Langevin equation.\n  We present a version of this convergence which is both simpler and stronger than the formulations which we know. Our main result s","authors_text":"Jan Derezinski, Wojciech De Roeck","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-10-22T21:15:54Z","title":"Extended Weak Coupling Limit for Pauli-Fierz Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0610054","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":"sha256:193d887a51153e07665d904950be03036c3186a503d83598ff58398c40df1ee9","target":"record","created_at":"2026-07-04T15:02:21Z","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":"2e774a1f558e91e90ad249535f497302a1c104d388e0eafe84e9192d686fafff","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-10-22T21:15:54Z","title_canon_sha256":"f2f1958c9eb6549a2abf6bb5b5031cd85c9c847e6c79ca0b3be0e4a9507a7487"},"schema_version":"1.0","source":{"id":"math-ph/0610054","kind":"arxiv","version":2}},"canonical_sha256":"43a702acf656b78652b5d4b54a317beb750dd01d52b7b1d2d61c45cc2be25f39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43a702acf656b78652b5d4b54a317beb750dd01d52b7b1d2d61c45cc2be25f39","first_computed_at":"2026-07-04T15:02:21.081970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:21.081970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GOZaP9iIdRpd1GABC//XbcmVsJnHnyYxvxjpD69LGOcYdzMbUav5mfCP8vWOhz1OagnNB5IlNEXeQNT5H3ZdCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:21.082321Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0610054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:193d887a51153e07665d904950be03036c3186a503d83598ff58398c40df1ee9","sha256:a6d1f816ee967b21e03a5470465ce7aa66a9de4f26414efc8a3b6ebcfe5899ba"],"state_sha256":"0b2c0c257155eab45ecc1df9e659890fbb706c0cc7023fe5ad0c8f6b78e7a22d"}