{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZDZ33VKFZ3Z24II7V2XRWGT2JO","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":"5209090f9afd7032c9d3fc2956b6f4aca89ad0585aa9e0fb786c4e23969d5ecc","cross_cats_sorted":["math-ph","math.FA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-09-07T10:45:44Z","title_canon_sha256":"4b402d8e945ff8bb61f2848a936d2c3baa33e3605e1dae77b040d645554a3ac5"},"schema_version":"1.0","source":{"id":"0909.1211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1211","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1211v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1211","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZDZ33VKFZ3Z2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZDZ33VKFZ3Z24II7","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZDZ33VKF","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c738ed18498ceae4627d52d8745166254ad8495cc43a1b45645d825c8b210a3f","target":"graph","created_at":"2026-05-18T04:10:09Z","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 a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J. We establish optimal estimates on the position of the spectrum of L with respect to the spectrum of A and we obtain norm bounds on the operator angles between maximal uniformly definite reducing subspaces of the unperturbed operator A and the perturbed operator L. All the bounds are given in terms of the norm of V and the distances between pairs of disjoint s","authors_text":"Alexander K. Motovilov, Christiane Tretter, Sergio Albeverio","cross_cats":["math-ph","math.FA","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-09-07T10:45:44Z","title":"Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1211","kind":"arxiv","version":1},"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":"sha256:18c84162b510485b41e1084be78b1ccf17bdec73862b2cf60aa5b68545a7f5ed","target":"record","created_at":"2026-05-18T04:10:09Z","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":"5209090f9afd7032c9d3fc2956b6f4aca89ad0585aa9e0fb786c4e23969d5ecc","cross_cats_sorted":["math-ph","math.FA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-09-07T10:45:44Z","title_canon_sha256":"4b402d8e945ff8bb61f2848a936d2c3baa33e3605e1dae77b040d645554a3ac5"},"schema_version":"1.0","source":{"id":"0909.1211","kind":"arxiv","version":1}},"canonical_sha256":"c8f3bdd545cef3ae211faeaf1b1a7a4ba7477dc5ed45517bd4bb16f6877f73ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8f3bdd545cef3ae211faeaf1b1a7a4ba7477dc5ed45517bd4bb16f6877f73ba","first_computed_at":"2026-05-18T04:10:09.233203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.233203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wiNg00RwsRHCzICGUS5U4WIXKK3SLvl3OID71ZR5v89pzj7nh0oZSh1QGHjZaRcDoJ5IEL7t4espbkEcXuv5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.233943Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18c84162b510485b41e1084be78b1ccf17bdec73862b2cf60aa5b68545a7f5ed","sha256:c738ed18498ceae4627d52d8745166254ad8495cc43a1b45645d825c8b210a3f"],"state_sha256":"f2ab4b060412f86e4caf809aaebe6953e68d2f07f46de5841b343c4bbc6138ff"}