{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:3UEY6WAQMJSIND3CRQWIWDYAPP","short_pith_number":"pith:3UEY6WAQ","schema_version":"1.0","canonical_sha256":"dd098f58106264868f628c2c8b0f007bd7f2024a05d890c8a4ff391c87607f70","source":{"kind":"arxiv","id":"math/0602251","version":1},"attestation_state":"computed","paper":{"title":"Comparison Theorems of Kolmogorov Type for Classes Defined by Cyclic Variation Diminishing Operators and Their Application","license":"","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Gensun Fang, Xuehua Li","submitted_at":"2006-02-12T09:57:24Z","abstract_excerpt":"Using present a unified approach, we establish a Kolmogorov type comparison theorem for the classes of $2\\pi$-periodic functions defined by a special class of operators having certain oscillation properties, which includes the classical Sobolev class of functions with 2$\\pi$-periodic, the Achieser class, and the Hardy-Sobolev class as its special examples. Then, using these results, we prove a Taikov type inequality, and calculate the exact values of Kolmogorov, Gel$'$fand, linear and information $n$--widths of this class of functions in some space $L_{q}$, which is the classical Lebesgue inte"},"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/0602251","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-02-12T09:57:24Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"3bdcfb9fd5e197cf315bf554b9b40068fe93ff3b65b88c2516d959d7c7d9e206","abstract_canon_sha256":"84f1287a6163e1b078fa81559f0c9992f12598b6e36b55604a12152293b1647d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:18.959644Z","signature_b64":"+XUkAdvNurdR5+7t3yLVQqsqY/G+oBqS0vJYea6iNvC63/SXre7WISQzwBvFcrg4w9hashaW51w36Dd8qLeIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd098f58106264868f628c2c8b0f007bd7f2024a05d890c8a4ff391c87607f70","last_reissued_at":"2026-06-03T22:06:18.959257Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:18.959257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison Theorems of Kolmogorov Type for Classes Defined by Cyclic Variation Diminishing Operators and Their Application","license":"","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Gensun Fang, Xuehua Li","submitted_at":"2006-02-12T09:57:24Z","abstract_excerpt":"Using present a unified approach, we establish a Kolmogorov type comparison theorem for the classes of $2\\pi$-periodic functions defined by a special class of operators having certain oscillation properties, which includes the classical Sobolev class of functions with 2$\\pi$-periodic, the Achieser class, and the Hardy-Sobolev class as its special examples. Then, using these results, we prove a Taikov type inequality, and calculate the exact values of Kolmogorov, Gel$'$fand, linear and information $n$--widths of this class of functions in some space $L_{q}$, which is the classical Lebesgue inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602251","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0602251/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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/0602251","created_at":"2026-06-03T22:06:18.959320+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0602251v1","created_at":"2026-06-03T22:06:18.959320+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602251","created_at":"2026-06-03T22:06:18.959320+00:00"},{"alias_kind":"pith_short_12","alias_value":"3UEY6WAQMJSI","created_at":"2026-06-03T22:06:18.959320+00:00"},{"alias_kind":"pith_short_16","alias_value":"3UEY6WAQMJSIND3C","created_at":"2026-06-03T22:06:18.959320+00:00"},{"alias_kind":"pith_short_8","alias_value":"3UEY6WAQ","created_at":"2026-06-03T22:06:18.959320+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/3UEY6WAQMJSIND3CRQWIWDYAPP","json":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP.json","graph_json":"https://pith.science/api/pith-number/3UEY6WAQMJSIND3CRQWIWDYAPP/graph.json","events_json":"https://pith.science/api/pith-number/3UEY6WAQMJSIND3CRQWIWDYAPP/events.json","paper":"https://pith.science/paper/3UEY6WAQ"},"agent_actions":{"view_html":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP","download_json":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP.json","view_paper":"https://pith.science/paper/3UEY6WAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0602251&json=true","fetch_graph":"https://pith.science/api/pith-number/3UEY6WAQMJSIND3CRQWIWDYAPP/graph.json","fetch_events":"https://pith.science/api/pith-number/3UEY6WAQMJSIND3CRQWIWDYAPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP/action/storage_attestation","attest_author":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP/action/author_attestation","sign_citation":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP/action/citation_signature","submit_replication":"https://pith.science/pith/3UEY6WAQMJSIND3CRQWIWDYAPP/action/replication_record"}},"created_at":"2026-06-03T22:06:18.959320+00:00","updated_at":"2026-06-03T22:06:18.959320+00:00"}