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Let $X$ be an infinite-dimensional Fr\\'echet space and let $\\mathcal{V}=\\{V_n\\}$ be a nested sequence of subspaces of $ X$ such that $ \\bar{V_n} \\subseteq V_{n+1}$ for any $ n \\in \\mathbb{N}$ and $\nX=\\bar{\\bigcup_{n=1}^{\\infty}V_n}.$\nLet $ e_n$ be a decreasing sequence of positive numbers tending to 0. Under an additional natural condition on $\\sup\\{\\{dist}(x, V_n)\\}$, we prove that there exists $ x \\in X$ and $ n_o \\in \\mathbb{N}$ such that $$ \\frac{e_n}{3} \\leq \\{dist}(x,V_n) \\leq 3 e_n $$ for "},"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":"1503.06190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-20T18:43:03Z","cross_cats_sorted":[],"title_canon_sha256":"37bf95617bc1ca847d9d8d1c89736b2db82dd3e3bedc8b51972c025876d9f8dd","abstract_canon_sha256":"2e367a901f3acf8728111ebc2870a214cfaab4dd49413d98803ab13d2d8b2166"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.371073Z","signature_b64":"6Nx1YqSysgeZQgjbPFoQu3nzzHwTnAFuiUbc/j1kskwVr/MoDaWIJKDtVd8mIw++SPzGqBKSWn26Thn0N5G4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50ee7287b62a214a0babe47b2a557100067a899ca963b0dd09953f50bbf91622","last_reissued_at":"2026-05-18T02:20:48.370331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.370331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernstein's Lethargy Theorem in Frechet Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asuman Guven Aksoy, Grzegorz Lewicki","submitted_at":"2015-03-20T18:43:03Z","abstract_excerpt":"In this paper we consider Bernstein's Lethargy Theorem (BLT) in the context of Fr\\'{e}chet spaces. 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Under an additional natural condition on $\\sup\\{\\{dist}(x, V_n)\\}$, we prove that there exists $ x \\in X$ and $ n_o \\in \\mathbb{N}$ such that $$ \\frac{e_n}{3} \\leq \\{dist}(x,V_n) \\leq 3 e_n $$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06190","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":"1503.06190","created_at":"2026-05-18T02:20:48.370463+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06190v1","created_at":"2026-05-18T02:20:48.370463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06190","created_at":"2026-05-18T02:20:48.370463+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDXHFB5WFIQU","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDXHFB5WFIQUUC5L","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDXHFB5W","created_at":"2026-05-18T12:29:27.538025+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/KDXHFB5WFIQUUC5L4R5SUVLRAA","json":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA.json","graph_json":"https://pith.science/api/pith-number/KDXHFB5WFIQUUC5L4R5SUVLRAA/graph.json","events_json":"https://pith.science/api/pith-number/KDXHFB5WFIQUUC5L4R5SUVLRAA/events.json","paper":"https://pith.science/paper/KDXHFB5W"},"agent_actions":{"view_html":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA","download_json":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA.json","view_paper":"https://pith.science/paper/KDXHFB5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06190&json=true","fetch_graph":"https://pith.science/api/pith-number/KDXHFB5WFIQUUC5L4R5SUVLRAA/graph.json","fetch_events":"https://pith.science/api/pith-number/KDXHFB5WFIQUUC5L4R5SUVLRAA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA/action/storage_attestation","attest_author":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA/action/author_attestation","sign_citation":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA/action/citation_signature","submit_replication":"https://pith.science/pith/KDXHFB5WFIQUUC5L4R5SUVLRAA/action/replication_record"}},"created_at":"2026-05-18T02:20:48.370463+00:00","updated_at":"2026-05-18T02:20:48.370463+00:00"}