{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WHRCG3TDUAI5EYNUV2XZYA4VUR","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":"10f66d77043acd1c2c6b2cbf4882146de0a82a5aaeac5f42f90648d92d7bc1d5","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-30T14:32:41Z","title_canon_sha256":"12421355313f378055068c9a7068bd89e5987b5387581b53f7f4f47b5bf459a4"},"schema_version":"1.0","source":{"id":"1710.10975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10975","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10975v1","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10975","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"WHRCG3TDUAI5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WHRCG3TDUAI5EYNU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WHRCG3TD","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:e59f0fd5783cd0879e9f87cc782e5f3262e8e1f2022f7bd174ff9a798ae694da","target":"graph","created_at":"2026-05-18T00:31:45Z","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 generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.","authors_text":"Christoph Uebersohn, Olaf Post","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-30T14:32:41Z","title":"On a generalisation of Krein's example"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10975","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":"sha256:667b62d1378b69447bfff2b1cd7bd080be118d522a93f10e86414da206874828","target":"record","created_at":"2026-05-18T00:31:45Z","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":"10f66d77043acd1c2c6b2cbf4882146de0a82a5aaeac5f42f90648d92d7bc1d5","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-30T14:32:41Z","title_canon_sha256":"12421355313f378055068c9a7068bd89e5987b5387581b53f7f4f47b5bf459a4"},"schema_version":"1.0","source":{"id":"1710.10975","kind":"arxiv","version":1}},"canonical_sha256":"b1e2236e63a011d261b4aeaf9c0395a44f55ecf539896b4954ed0a78a8da1dbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1e2236e63a011d261b4aeaf9c0395a44f55ecf539896b4954ed0a78a8da1dbb","first_computed_at":"2026-05-18T00:31:45.975504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:45.975504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Az5MXcsU6Qdo5Wii/2MhyAzrXZjVGadPCCR3m7cYO/mxSebeNjKR1I0DX6zbaVNmcZ+yiybhYDNlmu30P/EpCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:45.976152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:667b62d1378b69447bfff2b1cd7bd080be118d522a93f10e86414da206874828","sha256:e59f0fd5783cd0879e9f87cc782e5f3262e8e1f2022f7bd174ff9a798ae694da"],"state_sha256":"09a4b87a979df7287c67414a7820718ec9ca0621e5c8710d45cb8a0ab3e30693"}