{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GYON6UTFIEXJW5BX6W4J7D5SIG","short_pith_number":"pith:GYON6UTF","schema_version":"1.0","canonical_sha256":"361cdf5265412e9b7437f5b89f8fb24188ffbb66cbabc74b0a3fa28c29682533","source":{"kind":"arxiv","id":"1405.5414","version":1},"attestation_state":"computed","paper":{"title":"Perturbation of $\\ell_1$-copies in Preduals of JBW$^*$-triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Hermann Pfitzner (MAPMO)","submitted_at":"2014-05-21T13:28:07Z","abstract_excerpt":"Two normal functionals on a JBW$^*$-triple are known to be orthogonal if and only if they are $L$-orthogonal (meaning that they span an isometric copy of $\\ell_1(2)$). This is shown to be stable under small norm perturbations in the following sense: if the linear span of the two functionals is isometric up to $\\delta>0$ to $\\ell_1(2)$, then the functionals are less far (in norm) than $\\eps>0$ from two orthogonal functionals, where $\\eps\\to0$ as $\\delta\\to0$. Analogous statements for finitely and even infinitely many functionals hold as well. And so does a corresponding statement for non-normal"},"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":"1405.5414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-05-21T13:28:07Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"853b0978ccc531a9636434579f6127faf969bd7d5f7934f048e7734752b71f64","abstract_canon_sha256":"84d59e363ab761c6a5fcecc3aa5a422ccfa6ef2e6f78664993f37c21e179ef07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:24.278382Z","signature_b64":"qMf4bZSpBbVUeuRScDmyDgHvfPU34LG4zR6he2nIIhqHniVHECLJNtIijfhgL9pQjEo/Xh/BrSAwLsO/jhFPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"361cdf5265412e9b7437f5b89f8fb24188ffbb66cbabc74b0a3fa28c29682533","last_reissued_at":"2026-05-18T02:51:24.277684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:24.277684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbation of $\\ell_1$-copies in Preduals of JBW$^*$-triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Hermann Pfitzner (MAPMO)","submitted_at":"2014-05-21T13:28:07Z","abstract_excerpt":"Two normal functionals on a JBW$^*$-triple are known to be orthogonal if and only if they are $L$-orthogonal (meaning that they span an isometric copy of $\\ell_1(2)$). This is shown to be stable under small norm perturbations in the following sense: if the linear span of the two functionals is isometric up to $\\delta>0$ to $\\ell_1(2)$, then the functionals are less far (in norm) than $\\eps>0$ from two orthogonal functionals, where $\\eps\\to0$ as $\\delta\\to0$. Analogous statements for finitely and even infinitely many functionals hold as well. And so does a corresponding statement for non-normal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5414","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":"1405.5414","created_at":"2026-05-18T02:51:24.277779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5414v1","created_at":"2026-05-18T02:51:24.277779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5414","created_at":"2026-05-18T02:51:24.277779+00:00"},{"alias_kind":"pith_short_12","alias_value":"GYON6UTFIEXJ","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GYON6UTFIEXJW5BX","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GYON6UTF","created_at":"2026-05-18T12:28:30.664211+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/GYON6UTFIEXJW5BX6W4J7D5SIG","json":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG.json","graph_json":"https://pith.science/api/pith-number/GYON6UTFIEXJW5BX6W4J7D5SIG/graph.json","events_json":"https://pith.science/api/pith-number/GYON6UTFIEXJW5BX6W4J7D5SIG/events.json","paper":"https://pith.science/paper/GYON6UTF"},"agent_actions":{"view_html":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG","download_json":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG.json","view_paper":"https://pith.science/paper/GYON6UTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5414&json=true","fetch_graph":"https://pith.science/api/pith-number/GYON6UTFIEXJW5BX6W4J7D5SIG/graph.json","fetch_events":"https://pith.science/api/pith-number/GYON6UTFIEXJW5BX6W4J7D5SIG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG/action/storage_attestation","attest_author":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG/action/author_attestation","sign_citation":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG/action/citation_signature","submit_replication":"https://pith.science/pith/GYON6UTFIEXJW5BX6W4J7D5SIG/action/replication_record"}},"created_at":"2026-05-18T02:51:24.277779+00:00","updated_at":"2026-05-18T02:51:24.277779+00:00"}