{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HMWTY3ZHHWI5HC6UMVXMGT4ET5","short_pith_number":"pith:HMWTY3ZH","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"},"canonical_sha256":"3b2d3c6f273d91d38bd4656ec34f849f410115e12081626ea3418959a645f227","source":{"kind":"arxiv","id":"1010.6090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.6090","created_at":"2026-05-18T04:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.6090v1","created_at":"2026-05-18T04:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6090","created_at":"2026-05-18T04:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"HMWTY3ZHHWI5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HMWTY3ZHHWI5HC6U","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HMWTY3ZH","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HMWTY3ZHHWI5HC6UMVXMGT4ET5","target":"record","payload":{"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"},"canonical_sha256":"3b2d3c6f273d91d38bd4656ec34f849f410115e12081626ea3418959a645f227","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"},"source_kind":"arxiv","source_id":"1010.6090","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nfi8yWvzk7bcop2AiSxAMv2JWhfUwemF7qfr2pCsjQynLJAWW7aMNrOrYRCLMWLCxYGpTvF1vDogLVvsN/ydBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:58:00.388871Z"},"content_sha256":"26f3155df8c389b906102d4cd867100bed597511d381b8665a37f9bdcc2216f8","schema_version":"1.0","event_id":"sha256:26f3155df8c389b906102d4cd867100bed597511d381b8665a37f9bdcc2216f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HMWTY3ZHHWI5HC6UMVXMGT4ET5","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CxGmzES91vMK/sA+tfToWVmT0na4GXN22NmmDURQnajbQCkvmCzB1JMSCaIosptuta2VdGU0RdWXaoCXFTrwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:58:00.389213Z"},"content_sha256":"0e8c6b148656d1686a601db13a93e7eb57668ffb1bf4f54f712e7a08073fe084","schema_version":"1.0","event_id":"sha256:0e8c6b148656d1686a601db13a93e7eb57668ffb1bf4f54f712e7a08073fe084"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/bundle.json","state_url":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T14:58:00Z","links":{"resolver":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5","bundle":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/bundle.json","state":"https://pith.science/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMWTY3ZHHWI5HC6UMVXMGT4ET5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HMWTY3ZHHWI5HC6UMVXMGT4ET5","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":"18f27ec2aa6f2338a690f4a38cacc81f489aaa96f9b96545ef288204383180e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-28T20:40:58Z","title_canon_sha256":"ea9d528ae97763040e6d16b8ff4f7d63561fdaf854bd1bacf7626ba632f8e68a"},"schema_version":"1.0","source":{"id":"1010.6090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.6090","created_at":"2026-05-18T04:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.6090v1","created_at":"2026-05-18T04:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6090","created_at":"2026-05-18T04:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"HMWTY3ZHHWI5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HMWTY3ZHHWI5HC6U","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HMWTY3ZH","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:0e8c6b148656d1686a601db13a93e7eb57668ffb1bf4f54f712e7a08073fe084","target":"graph","created_at":"2026-05-18T04:38:07Z","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 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","authors_text":"Nikolai Nikolski, Vasily Vasyunin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-28T20:40:58Z","title":"Invertibility threshold for $H^\\infty$ trace algebras, and effective matrix inversions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6090","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":"sha256:26f3155df8c389b906102d4cd867100bed597511d381b8665a37f9bdcc2216f8","target":"record","created_at":"2026-05-18T04:38:07Z","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":"18f27ec2aa6f2338a690f4a38cacc81f489aaa96f9b96545ef288204383180e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-28T20:40:58Z","title_canon_sha256":"ea9d528ae97763040e6d16b8ff4f7d63561fdaf854bd1bacf7626ba632f8e68a"},"schema_version":"1.0","source":{"id":"1010.6090","kind":"arxiv","version":1}},"canonical_sha256":"3b2d3c6f273d91d38bd4656ec34f849f410115e12081626ea3418959a645f227","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b2d3c6f273d91d38bd4656ec34f849f410115e12081626ea3418959a645f227","first_computed_at":"2026-05-18T04:38:07.500189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:07.500189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fuf7lu1q84vw+pmevH957tFSiW2LymJH8xYagyKoyV1tHF/4ld/gNXJDCmHvIHmcTDT1jw3QwVDF+DVIGzbSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:07.500676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.6090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26f3155df8c389b906102d4cd867100bed597511d381b8665a37f9bdcc2216f8","sha256:0e8c6b148656d1686a601db13a93e7eb57668ffb1bf4f54f712e7a08073fe084"],"state_sha256":"e12a2977f255dbe7f0c41a637ef2547d78d1c28073f7f72f9f399121c30b6e86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Vk9Wz1LcjH4aXChtYXYlnIWCSZ4j4OVAx2dYvdbhNeTQ0zjr9m8SUgbNUYh8LC0TBh+amysjQpMSyvCZ1MdAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:58:00.391146Z","bundle_sha256":"74306a8ff5bd32dde58e7646f81f9139f247a24dc5deef013b4f5317e32b6f23"}}