{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KONNFRZLTU3UWLPRMUHBTVEOGD","short_pith_number":"pith:KONNFRZL","schema_version":"1.0","canonical_sha256":"539ad2c72b9d374b2df1650e19d48e30d0f8e9c2d219d94752ded4b670554e06","source":{"kind":"arxiv","id":"1710.10832","version":3},"attestation_state":"computed","paper":{"title":"Gradient Estimates on Dirichlet Eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Thalmaier, Feng-Yu Wang (TJU), Marc Arnaudon (IMB)","submitted_at":"2017-10-30T09:49:17Z","abstract_excerpt":"By methods of stochastic analysis on Riemannian manifolds, we derive explicit constants $c\\_1(D)$ and $c\\_2(D)$ for a $d$-dimensional compact Riemannian manifold $D$ with boundary such that $c\\_1(D)\\sqrt{\\lambda}\\|\\phi\\|\\_\\infty \\le \\|\\nabla \\phi\\|\\_\\infty\\le c\\_2(D)\\sqrt{\\lambda} \\|\\phi\\|\\_\\infty$ holds for any Dirichlet eigenfunction $\\phi$ of $-\\Delta$ with eigenvalue $\\lambda$. In particular, when $D$ is convex with nonnegative Ricci curvature, this estimate holds for $c\\_1(D)=\\frac{1}{de}$ and $c\\_2(D)=\\sqrt{e}\\left(\\frac{\\sqrt{2}}{\\sqrt{\\pi}}+\\frac{\\sqrt{\\pi}}{4\\sqrt{2}}\\right)$.  Corres"},"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":"1710.10832","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-30T09:49:17Z","cross_cats_sorted":[],"title_canon_sha256":"532a343bb782acce0a786f86cb3331cfd46c50fab002358a6e5be5c75fefa4cf","abstract_canon_sha256":"1418fe4d4c4bd3be263199e96618f2468fa0ebb0ea10191e763ec0c4e68050c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:21.465790Z","signature_b64":"Cbk+t2+Xfj8o++4LwXuP7UIyLYgbuN+95zQXocFIufn1Opl/KEHsFEXZwK7L8sUDsK2j0jvf6/H69uwiNaHGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"539ad2c72b9d374b2df1650e19d48e30d0f8e9c2d219d94752ded4b670554e06","last_reissued_at":"2026-05-18T00:08:21.465135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:21.465135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradient Estimates on Dirichlet Eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Thalmaier, Feng-Yu Wang (TJU), Marc Arnaudon (IMB)","submitted_at":"2017-10-30T09:49:17Z","abstract_excerpt":"By methods of stochastic analysis on Riemannian manifolds, we derive explicit constants $c\\_1(D)$ and $c\\_2(D)$ for a $d$-dimensional compact Riemannian manifold $D$ with boundary such that $c\\_1(D)\\sqrt{\\lambda}\\|\\phi\\|\\_\\infty \\le \\|\\nabla \\phi\\|\\_\\infty\\le c\\_2(D)\\sqrt{\\lambda} \\|\\phi\\|\\_\\infty$ holds for any Dirichlet eigenfunction $\\phi$ of $-\\Delta$ with eigenvalue $\\lambda$. In particular, when $D$ is convex with nonnegative Ricci curvature, this estimate holds for $c\\_1(D)=\\frac{1}{de}$ and $c\\_2(D)=\\sqrt{e}\\left(\\frac{\\sqrt{2}}{\\sqrt{\\pi}}+\\frac{\\sqrt{\\pi}}{4\\sqrt{2}}\\right)$.  Corres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10832","kind":"arxiv","version":3},"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":"1710.10832","created_at":"2026-05-18T00:08:21.465225+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10832v3","created_at":"2026-05-18T00:08:21.465225+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10832","created_at":"2026-05-18T00:08:21.465225+00:00"},{"alias_kind":"pith_short_12","alias_value":"KONNFRZLTU3U","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KONNFRZLTU3UWLPR","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KONNFRZL","created_at":"2026-05-18T12:31:24.725408+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/KONNFRZLTU3UWLPRMUHBTVEOGD","json":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD.json","graph_json":"https://pith.science/api/pith-number/KONNFRZLTU3UWLPRMUHBTVEOGD/graph.json","events_json":"https://pith.science/api/pith-number/KONNFRZLTU3UWLPRMUHBTVEOGD/events.json","paper":"https://pith.science/paper/KONNFRZL"},"agent_actions":{"view_html":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD","download_json":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD.json","view_paper":"https://pith.science/paper/KONNFRZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10832&json=true","fetch_graph":"https://pith.science/api/pith-number/KONNFRZLTU3UWLPRMUHBTVEOGD/graph.json","fetch_events":"https://pith.science/api/pith-number/KONNFRZLTU3UWLPRMUHBTVEOGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD/action/storage_attestation","attest_author":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD/action/author_attestation","sign_citation":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD/action/citation_signature","submit_replication":"https://pith.science/pith/KONNFRZLTU3UWLPRMUHBTVEOGD/action/replication_record"}},"created_at":"2026-05-18T00:08:21.465225+00:00","updated_at":"2026-05-18T00:08:21.465225+00:00"}