{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HMWTY3ZHHWI5HC6UMVXMGT4ET5","short_pith_number":"pith:HMWTY3ZH","schema_version":"1.0","canonical_sha256":"3b2d3c6f273d91d38bd4656ec34f849f410115e12081626ea3418959a645f227","source":{"kind":"arxiv","id":"1010.6090","version":1},"attestation_state":"computed","paper":{"title":"Invertibility threshold for $H^\\infty$ trace algebras, and effective matrix inversions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nikolai Nikolski, Vasily Vasyunin","submitted_at":"2010-10-28T20:40:58Z","abstract_excerpt":"For a given $\\delta$, $0<\\delta<1$, a Blaschke sequence $\\sigma=\\{\\lambda_j\\}$ is constructed such that every function $f$, $f\\in H^\\infty$, having $\\delta<\\delta_f=\\inf_{\\lambda\\in\\sigma}|f(\\lambda)|\\le\\|f\\|_\\infty\\le1$ is invertible in the trace algebra $H^\\infty|\\sigma$ (with a norm estimate of the inverse depending on $\\delta_f$ only), but there exists $f$ with $\\delta=\\delta_f\\le\\|f\\|_\\infty\\le1$, which does not. As an application, a counterexample to a stronger form of the Bourgain--Tzafriri restricted invertibility conjecture for bounded operators is exhibited, where an ``orthogonal (or"},"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":"1010.6090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-28T20:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"ea9d528ae97763040e6d16b8ff4f7d63561fdaf854bd1bacf7626ba632f8e68a","abstract_canon_sha256":"18f27ec2aa6f2338a690f4a38cacc81f489aaa96f9b96545ef288204383180e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:07.500676Z","signature_b64":"fuf7lu1q84vw+pmevH957tFSiW2LymJH8xYagyKoyV1tHF/4ld/gNXJDCmHvIHmcTDT1jw3QwVDF+DVIGzbSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b2d3c6f273d91d38bd4656ec34f849f410115e12081626ea3418959a645f227","last_reissued_at":"2026-05-18T04:38:07.500189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:07.500189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invertibility threshold for $H^\\infty$ trace algebras, and effective matrix inversions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nikolai Nikolski, Vasily Vasyunin","submitted_at":"2010-10-28T20:40:58Z","abstract_excerpt":"For a given $\\delta$, $0<\\delta<1$, a Blaschke sequence $\\sigma=\\{\\lambda_j\\}$ is constructed such that every function $f$, $f\\in H^\\infty$, having $\\delta<\\delta_f=\\inf_{\\lambda\\in\\sigma}|f(\\lambda)|\\le\\|f\\|_\\infty\\le1$ is invertible in the trace algebra $H^\\infty|\\sigma$ (with a norm estimate of the inverse depending on $\\delta_f$ only), but there exists $f$ with $\\delta=\\delta_f\\le\\|f\\|_\\infty\\le1$, which does not. As an application, a counterexample to a stronger form of the Bourgain--Tzafriri restricted invertibility conjecture for bounded operators is exhibited, where an ``orthogonal (or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6090","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":"1010.6090","created_at":"2026-05-18T04:38:07.500254+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.6090v1","created_at":"2026-05-18T04:38:07.500254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6090","created_at":"2026-05-18T04:38:07.500254+00:00"},{"alias_kind":"pith_short_12","alias_value":"HMWTY3ZHHWI5","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HMWTY3ZHHWI5HC6U","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HMWTY3ZH","created_at":"2026-05-18T12:26:07.630475+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/HMWTY3ZHHWI5HC6UMVXMGT4ET5","json":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5.json","graph_json":"https://pith.science/api/pith-number/HMWTY3ZHHWI5HC6UMVXMGT4ET5/graph.json","events_json":"https://pith.science/api/pith-number/HMWTY3ZHHWI5HC6UMVXMGT4ET5/events.json","paper":"https://pith.science/paper/HMWTY3ZH"},"agent_actions":{"view_html":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5","download_json":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5.json","view_paper":"https://pith.science/paper/HMWTY3ZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.6090&json=true","fetch_graph":"https://pith.science/api/pith-number/HMWTY3ZHHWI5HC6UMVXMGT4ET5/graph.json","fetch_events":"https://pith.science/api/pith-number/HMWTY3ZHHWI5HC6UMVXMGT4ET5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/action/storage_attestation","attest_author":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/action/author_attestation","sign_citation":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/action/citation_signature","submit_replication":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/action/replication_record"}},"created_at":"2026-05-18T04:38:07.500254+00:00","updated_at":"2026-05-18T04:38:07.500254+00:00"}