{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZH2NUM5Z6LULKASNREVI52JSO5","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":"1d668b1cf1506204cb246c8275e495fba5e8475a097133308e83848dee0df201","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2005-06-19T21:48:48Z","title_canon_sha256":"8576ba6ddcddeb95289e145fc32558a39f00eff5d95e61fea475a9a73fa04df7"},"schema_version":"1.0","source":{"id":"math/0506381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506381","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506381v2","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506381","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZH2NUM5Z6LUL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZH2NUM5Z6LULKASN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZH2NUM5Z","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7d9f29aa22b626a0d4243115b105faf27529eeb29a4ce8ae19fcf079f72a7129","target":"graph","created_at":"2026-05-18T03:59:49Z","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":"In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a $(\\lambda,\\beta)$-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.","authors_text":"B. Simonov, S. Tikhonov","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2005-06-19T21:48:48Z","title":"Embedding theorems of function classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506381","kind":"arxiv","version":2},"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":"sha256:6312e65c15e8bda42481ae0d447d3a665d9ba4c645115a38663c4b8475956bf1","target":"record","created_at":"2026-05-18T03:59:49Z","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":"1d668b1cf1506204cb246c8275e495fba5e8475a097133308e83848dee0df201","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2005-06-19T21:48:48Z","title_canon_sha256":"8576ba6ddcddeb95289e145fc32558a39f00eff5d95e61fea475a9a73fa04df7"},"schema_version":"1.0","source":{"id":"math/0506381","kind":"arxiv","version":2}},"canonical_sha256":"c9f4da33b9f2e8b5024d892a8ee932776c4d97796832f251c3a381ee4e6249bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9f4da33b9f2e8b5024d892a8ee932776c4d97796832f251c3a381ee4e6249bf","first_computed_at":"2026-05-18T03:59:49.858535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.858535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YHiZEaXVAJkY6Tc0ZYkAkWQZYPva6k7AeHwQ+eiERISXTcKpd8JmvfF4EeXg60DgadtLBgpr4jSDq0agBs0sCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.859016Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6312e65c15e8bda42481ae0d447d3a665d9ba4c645115a38663c4b8475956bf1","sha256:7d9f29aa22b626a0d4243115b105faf27529eeb29a4ce8ae19fcf079f72a7129"],"state_sha256":"71d3a49702d290e5115c8b5bf4fd8a95f1c4457ead29368159bd22f88553f464"}