{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GRYHEV47X5ZTJ5MW75RPEXB76Y","short_pith_number":"pith:GRYHEV47","schema_version":"1.0","canonical_sha256":"347072579fbf7334f596ff62f25c3ff60085ae7f1676dfe1aec3da6a82ed4f60","source":{"kind":"arxiv","id":"1410.3502","version":1},"attestation_state":"computed","paper":{"title":"On the Constant in The Lower Estimate for the Bernstein Operator","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gancho Tachev, Sorin Gal","submitted_at":"2014-10-13T20:22:02Z","abstract_excerpt":"For functions belonging to the classes $C^{2}[0, 1]$ and $C^{3}[0, 1]$, we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented."},"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":"1410.3502","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2014-10-13T20:22:02Z","cross_cats_sorted":[],"title_canon_sha256":"52f99c2cea87166375839093956e4f7471cb6aecf3b225f75d240781fc060307","abstract_canon_sha256":"9a43e26ea6974d83ac6c4376f92e97b37197a8bdba7780805250141a5afa0fb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:28.132480Z","signature_b64":"3cVdEIHOuXGMGyv+HWIpsou3Qpstx1EWwBxOtm7oOi6QrnxOBZOVRfcXc/6F4ISeVclKKa10jrROyCaL7p8rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"347072579fbf7334f596ff62f25c3ff60085ae7f1676dfe1aec3da6a82ed4f60","last_reissued_at":"2026-05-18T02:19:28.131942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:28.131942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Constant in The Lower Estimate for the Bernstein Operator","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gancho Tachev, Sorin Gal","submitted_at":"2014-10-13T20:22:02Z","abstract_excerpt":"For functions belonging to the classes $C^{2}[0, 1]$ and $C^{3}[0, 1]$, we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3502","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":"1410.3502","created_at":"2026-05-18T02:19:28.132015+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.3502v1","created_at":"2026-05-18T02:19:28.132015+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3502","created_at":"2026-05-18T02:19:28.132015+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRYHEV47X5ZT","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRYHEV47X5ZTJ5MW","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRYHEV47","created_at":"2026-05-18T12:28:30.664211+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/GRYHEV47X5ZTJ5MW75RPEXB76Y","json":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y.json","graph_json":"https://pith.science/api/pith-number/GRYHEV47X5ZTJ5MW75RPEXB76Y/graph.json","events_json":"https://pith.science/api/pith-number/GRYHEV47X5ZTJ5MW75RPEXB76Y/events.json","paper":"https://pith.science/paper/GRYHEV47"},"agent_actions":{"view_html":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y","download_json":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y.json","view_paper":"https://pith.science/paper/GRYHEV47","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.3502&json=true","fetch_graph":"https://pith.science/api/pith-number/GRYHEV47X5ZTJ5MW75RPEXB76Y/graph.json","fetch_events":"https://pith.science/api/pith-number/GRYHEV47X5ZTJ5MW75RPEXB76Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y/action/storage_attestation","attest_author":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y/action/author_attestation","sign_citation":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y/action/citation_signature","submit_replication":"https://pith.science/pith/GRYHEV47X5ZTJ5MW75RPEXB76Y/action/replication_record"}},"created_at":"2026-05-18T02:19:28.132015+00:00","updated_at":"2026-05-18T02:19:28.132015+00:00"}