{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7ZI55ROMALB666Q32BEI55QHFK","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":"952a8c4625fac0df7fe3f83bdcb12a0dd8a4bcc862a45010eb83bf03a42d921c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T07:48:46Z","title_canon_sha256":"ab4d7ddce3e919f42d23b38d458a736d2cea320942d0d41dc16f964eeae87138"},"schema_version":"1.0","source":{"id":"1105.3021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3021","created_at":"2026-05-18T01:49:56Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3021v1","created_at":"2026-05-18T01:49:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3021","created_at":"2026-05-18T01:49:56Z"},{"alias_kind":"pith_short_12","alias_value":"7ZI55ROMALB6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7ZI55ROMALB666Q3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7ZI55ROM","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:34e119d43b7c04049068b26afaae379c0a280482b7745b7dff05c30466bad16a","target":"graph","created_at":"2026-05-18T01:49:56Z","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 consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\\subset \\mathbb{R}^n$. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.","authors_text":"Gensun Fang, Shun Zhang","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T07:48:46Z","title":"Widths of embeddings of 2-microlocal Besov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3021","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:c29de1200bd298d180bd8047943ec89f0b02b46f1b05fde82dd2f33e3c54f09c","target":"record","created_at":"2026-05-18T01:49:56Z","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":"952a8c4625fac0df7fe3f83bdcb12a0dd8a4bcc862a45010eb83bf03a42d921c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T07:48:46Z","title_canon_sha256":"ab4d7ddce3e919f42d23b38d458a736d2cea320942d0d41dc16f964eeae87138"},"schema_version":"1.0","source":{"id":"1105.3021","kind":"arxiv","version":1}},"canonical_sha256":"fe51dec5cc02c3ef7a1bd0488ef6072a9429b7a9e8a73271f3c4f3b999597831","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe51dec5cc02c3ef7a1bd0488ef6072a9429b7a9e8a73271f3c4f3b999597831","first_computed_at":"2026-05-18T01:49:56.365693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:56.365693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2cDhX49DXxABRLAtBpPsfLmzEJtCwyiIgc0LX3FKVDxV//cXHkcJAQV6hYAhcOZmQDmSXzePI59LgU0zTVLlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:56.366303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c29de1200bd298d180bd8047943ec89f0b02b46f1b05fde82dd2f33e3c54f09c","sha256:34e119d43b7c04049068b26afaae379c0a280482b7745b7dff05c30466bad16a"],"state_sha256":"194929a77f963b75e71317aa8367e76c9e8186fcfc7dc97ad99f6e8ef452b0f0"}