{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BSEMB6CKVFHFXUWQXDOGXGGZJ4","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":"70d3e5ee3694e3966bfb0c1b24a20fd89173d676f9bedea180196249d5b6fe23","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-15T03:35:42Z","title_canon_sha256":"1ddf780f3511bc153ac43b06e1d262a19dbc857f98d19d104efe8cf936535937"},"schema_version":"1.0","source":{"id":"1308.3298","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3298","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3298v2","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3298","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"BSEMB6CKVFHF","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BSEMB6CKVFHFXUWQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BSEMB6CK","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:ccc7c96f512aaf116b1927ce0445fe64f399084d861b650530414af5f1a2469c","target":"graph","created_at":"2026-05-18T00:42:08Z","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":"For a unitary operator the family of its unitary perturbations by rank one operators with fixed range is parametrized by a complex parameter $\\gamma, |\\gamma|=1$. Namely all such unitary perturbations are $U_\\gamma:=U+(\\gamma-1) (., b_1)_{\\mathcal H} b$, where $b\\in\\mathcal H, \\|b\\|=1, b_1=U^{-1} b, |\\gamma|=1$. For $|\\gamma|<1$ operators $U_\\gamma$ are contractions with one-dimensional defects.\n  Restricting our attention on the non-trivial part of perturbation we assume that $b$ is cyclic for $U$. Then the operator $U_\\gamma$, $|\\gamma|<1$ is a completely non-unitary contraction, and thus un","authors_text":"Constanze Liaw, Sergei Treil","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-15T03:35:42Z","title":"Clark model in general situation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3298","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":"sha256:1070900568973cfc0d6adcefda80b31b9152f88ce66fe83054945c7fb4a2cef8","target":"record","created_at":"2026-05-18T00:42:08Z","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":"70d3e5ee3694e3966bfb0c1b24a20fd89173d676f9bedea180196249d5b6fe23","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-15T03:35:42Z","title_canon_sha256":"1ddf780f3511bc153ac43b06e1d262a19dbc857f98d19d104efe8cf936535937"},"schema_version":"1.0","source":{"id":"1308.3298","kind":"arxiv","version":2}},"canonical_sha256":"0c88c0f84aa94e5bd2d0b8dc6b98d94f04953c4d5eb7acef7dfda9763d2689d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c88c0f84aa94e5bd2d0b8dc6b98d94f04953c4d5eb7acef7dfda9763d2689d0","first_computed_at":"2026-05-18T00:42:08.102848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:08.102848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ZWsq8jSvIZ6IghLtq9Ky/IeCbvQn7Ar+tv4acHYk88cHRNHrtxz+ty/5be5vE2QqLQRIcVKiqT9oqNDac7YBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:08.103406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3298","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1070900568973cfc0d6adcefda80b31b9152f88ce66fe83054945c7fb4a2cef8","sha256:ccc7c96f512aaf116b1927ce0445fe64f399084d861b650530414af5f1a2469c"],"state_sha256":"a047783897152212f68b2f07b45374e0bd072913e5d7a6a5099accb65336ea6a"}