{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YTEQH2OVG52TUKP7DTJ2QLLOBY","short_pith_number":"pith:YTEQH2OV","schema_version":"1.0","canonical_sha256":"c4c903e9d537753a29ff1cd3a82d6e0e0f297b4f68bc69588538337828c77270","source":{"kind":"arxiv","id":"1412.1668","version":1},"attestation_state":"computed","paper":{"title":"Bernstein-Walsh inequalities in higher dimensions over exponential curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mark Lawrence, Shirali Kadyrov","submitted_at":"2014-12-04T14:02:19Z","abstract_excerpt":"Let ${{\\bf x}}=(x_1,\\dots,x_d) \\in [-1,1]^d$ be linearly independent over $\\mathbb Z$, set $K=\\{(e^{z},e^{x_1 z},e^{x_2 z}\\dots,e^{x_d z}): |z| \\le 1\\}.$ We prove sharp estimates for the growth of a polynomial of degree $n$, in terms of $$E_n({\\bf x}):=\\sup\\{\\|P\\|_{\\Delta^{d+1}}:P \\in \\mathcal P_n(d+1), \\|P\\|_K \\le 1\\},$$ where $\\Delta^{d+1}$ is the unit polydisk. For all ${{\\bf x}} \\in [-1,1]^d$ with linearly independent entries, we have the lower estimate $$\\log E_n({\\bf x})\\ge \\frac{n^{d+1}}{(d-1)!(d+1)} \\log n - O(n^{d+1});$$ for Diophantine $\\bf x$, we have $$\\log E_n({\\bf x})\\le \\frac{ n"},"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":"1412.1668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-12-04T14:02:19Z","cross_cats_sorted":[],"title_canon_sha256":"9a8e1ffde87d08110457059ec923fa89459a54cbb4565f3f60c8ff042e01d1af","abstract_canon_sha256":"76817e08d6081289bf7eaee8e09359f7a10e7c8adc7c5b5e4fcda0b0fe38779a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:06.757257Z","signature_b64":"9RlF+bHrPZMsx3nT6iwc8/eMK8u15OO/a0qNQ7W43xhlfjMRNfjmgN4ih7atSKMMht57kdFrNEV6Jqdu3Yp4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4c903e9d537753a29ff1cd3a82d6e0e0f297b4f68bc69588538337828c77270","last_reissued_at":"2026-05-18T02:32:06.756716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:06.756716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernstein-Walsh inequalities in higher dimensions over exponential curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mark Lawrence, Shirali Kadyrov","submitted_at":"2014-12-04T14:02:19Z","abstract_excerpt":"Let ${{\\bf x}}=(x_1,\\dots,x_d) \\in [-1,1]^d$ be linearly independent over $\\mathbb Z$, set $K=\\{(e^{z},e^{x_1 z},e^{x_2 z}\\dots,e^{x_d z}): |z| \\le 1\\}.$ We prove sharp estimates for the growth of a polynomial of degree $n$, in terms of $$E_n({\\bf x}):=\\sup\\{\\|P\\|_{\\Delta^{d+1}}:P \\in \\mathcal P_n(d+1), \\|P\\|_K \\le 1\\},$$ where $\\Delta^{d+1}$ is the unit polydisk. For all ${{\\bf x}} \\in [-1,1]^d$ with linearly independent entries, we have the lower estimate $$\\log E_n({\\bf x})\\ge \\frac{n^{d+1}}{(d-1)!(d+1)} \\log n - O(n^{d+1});$$ for Diophantine $\\bf x$, we have $$\\log E_n({\\bf x})\\le \\frac{ n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1668","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":"1412.1668","created_at":"2026-05-18T02:32:06.756796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1668v1","created_at":"2026-05-18T02:32:06.756796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1668","created_at":"2026-05-18T02:32:06.756796+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTEQH2OVG52T","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTEQH2OVG52TUKP7","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTEQH2OV","created_at":"2026-05-18T12:28:57.508820+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/YTEQH2OVG52TUKP7DTJ2QLLOBY","json":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY.json","graph_json":"https://pith.science/api/pith-number/YTEQH2OVG52TUKP7DTJ2QLLOBY/graph.json","events_json":"https://pith.science/api/pith-number/YTEQH2OVG52TUKP7DTJ2QLLOBY/events.json","paper":"https://pith.science/paper/YTEQH2OV"},"agent_actions":{"view_html":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY","download_json":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY.json","view_paper":"https://pith.science/paper/YTEQH2OV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1668&json=true","fetch_graph":"https://pith.science/api/pith-number/YTEQH2OVG52TUKP7DTJ2QLLOBY/graph.json","fetch_events":"https://pith.science/api/pith-number/YTEQH2OVG52TUKP7DTJ2QLLOBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY/action/storage_attestation","attest_author":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY/action/author_attestation","sign_citation":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY/action/citation_signature","submit_replication":"https://pith.science/pith/YTEQH2OVG52TUKP7DTJ2QLLOBY/action/replication_record"}},"created_at":"2026-05-18T02:32:06.756796+00:00","updated_at":"2026-05-18T02:32:06.756796+00:00"}