{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MZ65SQAYYRQ2XQI55ZMQD7WIJO","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":"80434c9d8306daf7de9000a89e592f99a50a8bf728c0466cb69e5913e7be2250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-09T13:21:42Z","title_canon_sha256":"f91adde99d2bf8f2b1c0fb57dea2cef1aa59703d911e9c00000f77d3c85427d7"},"schema_version":"1.0","source":{"id":"1112.2096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2096","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2096v1","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2096","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"MZ65SQAYYRQ2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MZ65SQAYYRQ2XQI5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MZ65SQAY","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:8862648c0887de77d4e94378e9fc15d69ab430b0637d291691c5c8a1511b8633","target":"graph","created_at":"2026-05-18T04:06:44Z","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":"We study the variation of the discrete spectrum of a bounded non-negative operator in a Krein space under a non-negative Schatten class perturbation of order $p$. It turns out that there exist so-called extended enumerations of discrete eigenvalues of the unperturbed and the perturbed operator, respectively, whose difference is an $\\ell^p$-sequence. This result is a Krein space version of a theorem by T.Kato for bounded selfadjoint operators in Hilbert spaces.","authors_text":"Friedrich Philipp, Jussi Behrndt, Leslie Leben","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-09T13:21:42Z","title":"Variation of discrete spectra of non-negative operators in Krein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2096","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":"sha256:34cc221735a2070aeb955291ba31d9e4b4569c6dc023e4154f6335de7e5ac314","target":"record","created_at":"2026-05-18T04:06:44Z","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":"80434c9d8306daf7de9000a89e592f99a50a8bf728c0466cb69e5913e7be2250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-09T13:21:42Z","title_canon_sha256":"f91adde99d2bf8f2b1c0fb57dea2cef1aa59703d911e9c00000f77d3c85427d7"},"schema_version":"1.0","source":{"id":"1112.2096","kind":"arxiv","version":1}},"canonical_sha256":"667dd94018c461abc11dee5901fec84b8ea77c8631db06f1ea235168d1b2983c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"667dd94018c461abc11dee5901fec84b8ea77c8631db06f1ea235168d1b2983c","first_computed_at":"2026-05-18T04:06:44.105452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:44.105452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ZbAD39Y7FkNSOJMLrcxrk5soTNiQsDd21CA/z2AheK1MjBJQJdtRr9AhgbeMXrRbt4z+s5DcT4Dd6w3qZ9UBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:44.105885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34cc221735a2070aeb955291ba31d9e4b4569c6dc023e4154f6335de7e5ac314","sha256:8862648c0887de77d4e94378e9fc15d69ab430b0637d291691c5c8a1511b8633"],"state_sha256":"fbfff6e86fa27df3ebf9c20cdde615a7c298969debe57b60ad0619d6dfdc8eca"}