{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1995:PBVNNAGR3ROOAVIQDIF7Y3N4SO","short_pith_number":"pith:PBVNNAGR","schema_version":"1.0","canonical_sha256":"786ad680d1dc5ce055101a0bfc6dbc93b61ebc345d836adadbf768f3a3305299","source":{"kind":"arxiv","id":"math/9511214","version":1},"attestation_state":"computed","paper":{"title":"Continuity properties of best analytic approximation","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nicholas J. Young, Vladimir V. Peller","submitted_at":"1995-11-28T00:00:00Z","abstract_excerpt":"Let $\\A$ be the operator which assigns to each $m \\times n$ matrix-valued function on the unit circle with entries in $H^\\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \\times n$ matrix-valued functions in the open unit disc. We study the continuity of $\\A$ with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, $\\A$ is continuous at any function whose superoptimal singular values are non-zero and is such that certain associated integer indices are equal to 1. We also obtain necessary conditions for cont"},"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":"math/9511214","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1995-11-28T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"81bfe63a3a82aa6db8550330ab13d49ca722412395eda301e8beb6599d034efc","abstract_canon_sha256":"a1800c691dea25ec434d8db42d70b6036138590d5a5598e854010dfd3a216668"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:48.117790Z","signature_b64":"g6m1nrG/FCovSm5sUsXLJW870+BlxTAv3mvd0qWRG78tQv9QmJVGhFvmAsdxKIwpgd9ssIo0kZZce9WahmWzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"786ad680d1dc5ce055101a0bfc6dbc93b61ebc345d836adadbf768f3a3305299","last_reissued_at":"2026-05-18T01:05:48.117062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:48.117062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity properties of best analytic approximation","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nicholas J. Young, Vladimir V. Peller","submitted_at":"1995-11-28T00:00:00Z","abstract_excerpt":"Let $\\A$ be the operator which assigns to each $m \\times n$ matrix-valued function on the unit circle with entries in $H^\\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \\times n$ matrix-valued functions in the open unit disc. We study the continuity of $\\A$ with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, $\\A$ is continuous at any function whose superoptimal singular values are non-zero and is such that certain associated integer indices are equal to 1. We also obtain necessary conditions for cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9511214","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":"math/9511214","created_at":"2026-05-18T01:05:48.117185+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9511214v1","created_at":"2026-05-18T01:05:48.117185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9511214","created_at":"2026-05-18T01:05:48.117185+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBVNNAGR3ROO","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBVNNAGR3ROOAVIQ","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBVNNAGR","created_at":"2026-05-18T12:25:47.700082+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/PBVNNAGR3ROOAVIQDIF7Y3N4SO","json":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO.json","graph_json":"https://pith.science/api/pith-number/PBVNNAGR3ROOAVIQDIF7Y3N4SO/graph.json","events_json":"https://pith.science/api/pith-number/PBVNNAGR3ROOAVIQDIF7Y3N4SO/events.json","paper":"https://pith.science/paper/PBVNNAGR"},"agent_actions":{"view_html":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO","download_json":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO.json","view_paper":"https://pith.science/paper/PBVNNAGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9511214&json=true","fetch_graph":"https://pith.science/api/pith-number/PBVNNAGR3ROOAVIQDIF7Y3N4SO/graph.json","fetch_events":"https://pith.science/api/pith-number/PBVNNAGR3ROOAVIQDIF7Y3N4SO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO/action/storage_attestation","attest_author":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO/action/author_attestation","sign_citation":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO/action/citation_signature","submit_replication":"https://pith.science/pith/PBVNNAGR3ROOAVIQDIF7Y3N4SO/action/replication_record"}},"created_at":"2026-05-18T01:05:48.117185+00:00","updated_at":"2026-05-18T01:05:48.117185+00:00"}