{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:443SQD2E3NSYN2ZX77DWUPYW6Y","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":"a29746f1e9b9aaffbe4e6b8af227a448defad2f257bda3146cea12b9ce464356","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-04-25T07:32:43Z","title_canon_sha256":"4a363accddba4ae8efe6dbe0bf6564b1cc68c200250e6bccbfee3a1d581ac598"},"schema_version":"1.0","source":{"id":"math-ph/0604058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0604058","created_at":"2026-07-04T17:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0604058v2","created_at":"2026-07-04T17:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0604058","created_at":"2026-07-04T17:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"443SQD2E3NSY","created_at":"2026-07-04T17:02:06Z"},{"alias_kind":"pith_short_16","alias_value":"443SQD2E3NSYN2ZX","created_at":"2026-07-04T17:02:06Z"},{"alias_kind":"pith_short_8","alias_value":"443SQD2E","created_at":"2026-07-04T17:02:06Z"}],"graph_snapshots":[{"event_id":"sha256:472a9d1d8d4918066d45805b01bbb14b1f1413104757b2c81d140b658588babc","target":"graph","created_at":"2026-07-04T17:02:06Z","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/0604058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a ``Friedrichs Hamiltonian'', has a small coupling constant in front of its off-diagonal term. It is well known that under some conditions in the weak coupling limit the appropriately rescaled evolution in the interaction picture converges to a contractive semigroup when restricted to the subsystem. We show that in this model, the properly renormalized and resca","authors_text":"Jan Derezinski, Wojciech De Roeck","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-04-25T07:32:43Z","title":"Extended Weak Coupling Limit for Friedrichs Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0604058","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":"sha256:961958f49a5b9980cfddd46b458dd87abc2a070d5d79a2c3c688544cde6f7891","target":"record","created_at":"2026-07-04T17:02:06Z","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":"a29746f1e9b9aaffbe4e6b8af227a448defad2f257bda3146cea12b9ce464356","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-04-25T07:32:43Z","title_canon_sha256":"4a363accddba4ae8efe6dbe0bf6564b1cc68c200250e6bccbfee3a1d581ac598"},"schema_version":"1.0","source":{"id":"math-ph/0604058","kind":"arxiv","version":2}},"canonical_sha256":"e737280f44db6586eb37ffc76a3f16f603900f81d77f9bb805953c33a3c42dba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e737280f44db6586eb37ffc76a3f16f603900f81d77f9bb805953c33a3c42dba","first_computed_at":"2026-07-04T17:02:06.204566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:02:06.204566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NjVLsp/QbVRq6vH2QyU0CKuM9KOpzXtmxjupOq+t01v124jOHRLeLBLOUZfi42YAlX0adM1cXaVcXKImSgBbDw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:02:06.204891Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0604058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:961958f49a5b9980cfddd46b458dd87abc2a070d5d79a2c3c688544cde6f7891","sha256:472a9d1d8d4918066d45805b01bbb14b1f1413104757b2c81d140b658588babc"],"state_sha256":"f96003787b002ed33ef6a828940d3cf68b26ee28cc1e3e1b21743e658fbc81d7"}