{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4T5TJ3DSEJQZD2TVF7TOYJB75I","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":"13f734cb0fcf0d48f7ccb2034c104f348da48feb66ab5be7c1b75bd953359ba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-13T07:39:33Z","title_canon_sha256":"da72c550a7fcdffd6f89acbe5abb51cbc9f87b4e64dbfb4f43505d22fef99747"},"schema_version":"1.0","source":{"id":"1409.3923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3923","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3923v1","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3923","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"4T5TJ3DSEJQZ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4T5TJ3DSEJQZD2TV","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4T5TJ3DS","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:d98e3036401355ad11f469bacb913c16ec8297421cf6d36718a9f47432fca2a7","target":"graph","created_at":"2026-05-18T02:42:53Z","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":"This paper concerns the approximation by the Boolean sums of Jackson operators $\\oplus^rJ_{k,s}(f)$ on the unit sphere $\\mathbb S^{n-1}$ of $\\mathbb{R}^{n}$. We prove the following the direct and inverse theorem for $\\oplus^rJ_{k,s}(f)$: there are constants $C_1$ and $C_2$ such that \\begin{equation*} C_1\\|\\oplus^rJ_{k,s}f-f\\|_p \\leq \\omega^{2r}(f,k^{-1})_p \\leq C_2 \\max_{v\\geq k}\\|\\oplus^rJ_{k,s}f-f\\|_p \\end{equation*} for any positive integer $k$ and any $p$th Lebesgue integrable functions $f$ defined on $\\mathbb S^{n-1}$, where $\\omega^{2r}(f,t)_p$ is the modulus of smoothness of degree $2r$","authors_text":"Feilong Cao, Yuguang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-13T07:39:33Z","title":"Approximation by boolean sums of Jackson operators on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3923","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":"sha256:2e5aae93a9077c5481b625b5b9edf91251be351191877c8986e7a33a003adaa2","target":"record","created_at":"2026-05-18T02:42:53Z","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":"13f734cb0fcf0d48f7ccb2034c104f348da48feb66ab5be7c1b75bd953359ba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-13T07:39:33Z","title_canon_sha256":"da72c550a7fcdffd6f89acbe5abb51cbc9f87b4e64dbfb4f43505d22fef99747"},"schema_version":"1.0","source":{"id":"1409.3923","kind":"arxiv","version":1}},"canonical_sha256":"e4fb34ec72226191ea752fe6ec243fea35a059a86056ef572b11aaf5f1ee1501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4fb34ec72226191ea752fe6ec243fea35a059a86056ef572b11aaf5f1ee1501","first_computed_at":"2026-05-18T02:42:53.376764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:53.376764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FMffx/ypnnljc4PPQd8ZNdJWbweD2RUqiYiEchEUQzCWm5WmwBhY74h8s4lguK2xjh2cqucY3evitc1TItudAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:53.377136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e5aae93a9077c5481b625b5b9edf91251be351191877c8986e7a33a003adaa2","sha256:d98e3036401355ad11f469bacb913c16ec8297421cf6d36718a9f47432fca2a7"],"state_sha256":"7acb64f3b00fca2315cdb11359f8c0cb36d2759ae46bd5ad9968b26d5d948666"}