{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AGYVAQEC43VGM3DN2O3U7ZCKNZ","short_pith_number":"pith:AGYVAQEC","schema_version":"1.0","canonical_sha256":"01b1504082e6ea666c6dd3b74fe44a6e514d07413b0ea449167679a2525c0978","source":{"kind":"arxiv","id":"1506.00072","version":1},"attestation_state":"computed","paper":{"title":"Singular integrals, rank one perturbations and Clark model in general situation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Constanze Liaw, Sergei Treil","submitted_at":"2015-05-30T04:45:09Z","abstract_excerpt":"We start with considering rank one self-adjoint perturbations $A_\\alpha = A+\\alpha(\\,\\cdot\\,,\\varphi)\\varphi$ with cyclic vector $\\varphi\\in \\mathcal{H}$ on a separable Hilbert space $\\mathcal H$. The spectral representation of the perturbed operator $A_\\alpha$ is realized by a (unitary) operator of a special type: the Hilbert transform in the two-weight setting, the weights being spectral measures of the operators $A$ and $A_\\alpha$.\n  Similar results will be presented for unitary rank one perturbations of unitary operators, leading to singular integral operators on the circle.\n  This motivat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.00072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-30T04:45:09Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d90a76f415ee67b4d574947313cf2809d05e0f72194cfed59e3be229af12ca27","abstract_canon_sha256":"15455e80fbbb4d93c09c20406d224cb9dcfc1daa9383a09de9ae7755683a03a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:07.930755Z","signature_b64":"mnkvsrook8dnZXUUN71K0BE6MJWUjJxuwrnE+ymu5ka//38NmnIifJbdLLJFl83LBF60o0ejEU9FJL817Y3LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01b1504082e6ea666c6dd3b74fe44a6e514d07413b0ea449167679a2525c0978","last_reissued_at":"2026-05-18T00:42:07.930196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:07.930196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular integrals, rank one perturbations and Clark model in general situation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Constanze Liaw, Sergei Treil","submitted_at":"2015-05-30T04:45:09Z","abstract_excerpt":"We start with considering rank one self-adjoint perturbations $A_\\alpha = A+\\alpha(\\,\\cdot\\,,\\varphi)\\varphi$ with cyclic vector $\\varphi\\in \\mathcal{H}$ on a separable Hilbert space $\\mathcal H$. The spectral representation of the perturbed operator $A_\\alpha$ is realized by a (unitary) operator of a special type: the Hilbert transform in the two-weight setting, the weights being spectral measures of the operators $A$ and $A_\\alpha$.\n  Similar results will be presented for unitary rank one perturbations of unitary operators, leading to singular integral operators on the circle.\n  This motivat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00072","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.00072","created_at":"2026-05-18T00:42:07.930292+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00072v1","created_at":"2026-05-18T00:42:07.930292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00072","created_at":"2026-05-18T00:42:07.930292+00:00"},{"alias_kind":"pith_short_12","alias_value":"AGYVAQEC43VG","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AGYVAQEC43VGM3DN","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AGYVAQEC","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ","json":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ.json","graph_json":"https://pith.science/api/pith-number/AGYVAQEC43VGM3DN2O3U7ZCKNZ/graph.json","events_json":"https://pith.science/api/pith-number/AGYVAQEC43VGM3DN2O3U7ZCKNZ/events.json","paper":"https://pith.science/paper/AGYVAQEC"},"agent_actions":{"view_html":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ","download_json":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ.json","view_paper":"https://pith.science/paper/AGYVAQEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00072&json=true","fetch_graph":"https://pith.science/api/pith-number/AGYVAQEC43VGM3DN2O3U7ZCKNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/AGYVAQEC43VGM3DN2O3U7ZCKNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ/action/storage_attestation","attest_author":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ/action/author_attestation","sign_citation":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ/action/citation_signature","submit_replication":"https://pith.science/pith/AGYVAQEC43VGM3DN2O3U7ZCKNZ/action/replication_record"}},"created_at":"2026-05-18T00:42:07.930292+00:00","updated_at":"2026-05-18T00:42:07.930292+00:00"}