{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VES7I2MC66Q4CZSRTYP65SJ3SE","short_pith_number":"pith:VES7I2MC","schema_version":"1.0","canonical_sha256":"a925f46982f7a1c166519e1feec93b91320197a2979560c5ab54a6a4ff998828","source":{"kind":"arxiv","id":"1809.09726","version":2},"attestation_state":"computed","paper":{"title":"Sharp Remez inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"P. Yuditskii, S. Tikhonov","submitted_at":"2018-09-25T21:11:52Z","abstract_excerpt":"Let an algebraic polynomial $P_n(\\zeta)$ of degree $n$ be such that $|P_n(\\zeta)|\\le 1$ for $\\zeta\\in E\\subset\\mathbb{T}$ and $|E|\\ge 2\\pi -s$. We prove the sharp Remez inequality $$ \\sup_{\\zeta\\in\\mathbb{T}}|P_n(\\zeta)|\\le \\mathfrak{T}_{n}\\left(\\sec \\frac{s} 4\\right),$$ where $\\mathfrak{T}_{n}$ is the Chebyshev polynomial of degree $n$. The equality holds if and only if $$ P_n(e^{iz})=e^{i(nz/2+c_1)}\\mathfrak{T}_n\\left(\\sec\\frac s 4\\cos \\frac {z-c_0} 2\\right), \\quad c_0,c_1\\in\\mathbb{R}. $$ This gives the solution of the long-standing problem on the sharp constant in the Remez inequality for "},"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":"1809.09726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-09-25T21:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"c30fe3eefef6f5d552f1e5904d9454bcd7fcb6012fe258f0cfb4e4a53f4faecb","abstract_canon_sha256":"2678b6d20d9919b9af583cee21573c564046ec322654464d0d60732395b0280c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:44.248043Z","signature_b64":"pZebxFftS/gD31V8VGfmJwm4lPo+1uFcqDVMZZ8aGrxBTrSHauLkkzhAFwXosdwjYef254Uejym7kGqUyB+yAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a925f46982f7a1c166519e1feec93b91320197a2979560c5ab54a6a4ff998828","last_reissued_at":"2026-05-18T00:02:44.247630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:44.247630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Remez inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"P. Yuditskii, S. Tikhonov","submitted_at":"2018-09-25T21:11:52Z","abstract_excerpt":"Let an algebraic polynomial $P_n(\\zeta)$ of degree $n$ be such that $|P_n(\\zeta)|\\le 1$ for $\\zeta\\in E\\subset\\mathbb{T}$ and $|E|\\ge 2\\pi -s$. We prove the sharp Remez inequality $$ \\sup_{\\zeta\\in\\mathbb{T}}|P_n(\\zeta)|\\le \\mathfrak{T}_{n}\\left(\\sec \\frac{s} 4\\right),$$ where $\\mathfrak{T}_{n}$ is the Chebyshev polynomial of degree $n$. The equality holds if and only if $$ P_n(e^{iz})=e^{i(nz/2+c_1)}\\mathfrak{T}_n\\left(\\sec\\frac s 4\\cos \\frac {z-c_0} 2\\right), \\quad c_0,c_1\\in\\mathbb{R}. $$ This gives the solution of the long-standing problem on the sharp constant in the Remez inequality for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09726","kind":"arxiv","version":2},"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":"1809.09726","created_at":"2026-05-18T00:02:44.247686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.09726v2","created_at":"2026-05-18T00:02:44.247686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09726","created_at":"2026-05-18T00:02:44.247686+00:00"},{"alias_kind":"pith_short_12","alias_value":"VES7I2MC66Q4","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VES7I2MC66Q4CZSR","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VES7I2MC","created_at":"2026-05-18T12:32:59.047623+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/VES7I2MC66Q4CZSRTYP65SJ3SE","json":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE.json","graph_json":"https://pith.science/api/pith-number/VES7I2MC66Q4CZSRTYP65SJ3SE/graph.json","events_json":"https://pith.science/api/pith-number/VES7I2MC66Q4CZSRTYP65SJ3SE/events.json","paper":"https://pith.science/paper/VES7I2MC"},"agent_actions":{"view_html":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE","download_json":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE.json","view_paper":"https://pith.science/paper/VES7I2MC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.09726&json=true","fetch_graph":"https://pith.science/api/pith-number/VES7I2MC66Q4CZSRTYP65SJ3SE/graph.json","fetch_events":"https://pith.science/api/pith-number/VES7I2MC66Q4CZSRTYP65SJ3SE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE/action/storage_attestation","attest_author":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE/action/author_attestation","sign_citation":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE/action/citation_signature","submit_replication":"https://pith.science/pith/VES7I2MC66Q4CZSRTYP65SJ3SE/action/replication_record"}},"created_at":"2026-05-18T00:02:44.247686+00:00","updated_at":"2026-05-18T00:02:44.247686+00:00"}