{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5PESESAD477NIBWEOXZ3HORYB5","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":"ee9569af730c26a231ec9a0dd95784b53924ab182b92d398ce05946951307a7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-02T16:03:43Z","title_canon_sha256":"cf04d62e723cbfb4d915bb6e427582ee2ef061178426d30721be72607528e265"},"schema_version":"1.0","source":{"id":"1606.00738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00738","created_at":"2026-05-18T01:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00738v1","created_at":"2026-05-18T01:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00738","created_at":"2026-05-18T01:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"5PESESAD477N","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5PESESAD477NIBWE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5PESESAD","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:9a6ce8395162fc24384c9985b2d0ea0df202344306c7762331ec7ec930aa81c5","target":"graph","created_at":"2026-05-18T01:13:03Z","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":"We prove that the cartesian product of octahedra $B_{1,\\infty}^{n,m}=B_1^n\\times\\ldots\\times B_1^n$ ($m$ octahedra) is badly approximated by half--dimensional subspaces in mixed--norm: $d_{N/2}(B_{1,\\infty}^{n,m},\\ell_{2,1}^{n,m})\\ge cm$, $N=mn$. As a corollary the orders for linear widths of H\\\"older--Nikolskii classes $H^r_p(\\mathbb T^d)$ in the $L_q$ metric are obtained for $(p,q)$ in a certain set (a domain in the parameter space).","authors_text":"K.S. Ryutin, Yu.V. Malykhin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-02T16:03:43Z","title":"Product of octahedra is badly approximated in the $\\ell_{2,1}$-metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00738","kind":"arxiv","version":1},"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:f6e4bdbed962dd58e3c6d9b32e5d44b3934fdef0840b4cf66c83dc8de382e6e7","target":"record","created_at":"2026-05-18T01:13:03Z","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":"ee9569af730c26a231ec9a0dd95784b53924ab182b92d398ce05946951307a7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-02T16:03:43Z","title_canon_sha256":"cf04d62e723cbfb4d915bb6e427582ee2ef061178426d30721be72607528e265"},"schema_version":"1.0","source":{"id":"1606.00738","kind":"arxiv","version":1}},"canonical_sha256":"ebc9224803e7fed406c475f3b3ba380f52b1f2a3dc1008f451e45f2581f72f25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebc9224803e7fed406c475f3b3ba380f52b1f2a3dc1008f451e45f2581f72f25","first_computed_at":"2026-05-18T01:13:03.855306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:03.855306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E3e9oOucUZMYotPxGnrEiWXhYUOPA6wAj+yoYIuMV0LOuF2udn71h+wueUKDt0a86bAKNcd30G5dNIlQPHmdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:03.855719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6e4bdbed962dd58e3c6d9b32e5d44b3934fdef0840b4cf66c83dc8de382e6e7","sha256:9a6ce8395162fc24384c9985b2d0ea0df202344306c7762331ec7ec930aa81c5"],"state_sha256":"35bce869d228aab838146cfff1259695160fc08a0110047c57d9b744cb4652c9"}