{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:R6NXEQ5DXWV7OKGHUPSDPW256Q","short_pith_number":"pith:R6NXEQ5D","schema_version":"1.0","canonical_sha256":"8f9b7243a3bdabf728c7a3e437db5df42185f28c95a342a368126de666b7c9f4","source":{"kind":"arxiv","id":"1905.08151","version":3},"attestation_state":"computed","paper":{"title":"An $L^p$-comparison, $p\\in (1,\\infty)$, on the finite differences of a discrete harmonic function at the boundary of a discrete box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.CA"],"primary_cat":"math.NA","authors_text":"Tuan Anh Nguyen","submitted_at":"2019-05-20T14:55:27Z","abstract_excerpt":"It is well-known that for a harmonic function $u$ defined on the unit ball of the $d$-dimensional Euclidean space, $d\\geq 2$, the tangential and normal component of the gradient $\\nabla u$ on the sphere are comparable by means of the $L^p$-norms, $p\\in(1,\\infty)$, up to multiplicative constants that depend only on $d,p$. This paper formulates and proves a discrete analogue of this result for discrete harmonic functions defined on a discrete box on the $d$-dimensional lattice with multiplicative constants that do not depend on the size of the box."},"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":"1905.08151","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-05-20T14:55:27Z","cross_cats_sorted":["cs.NA","math.AP","math.CA"],"title_canon_sha256":"93f9ab06317f807e249282a1bebdc6757eeb7f07d8d83cc503c3db76dc037047","abstract_canon_sha256":"f21bc967969df78cc99df416f0fb88db58eaad6a6e5df206c5526bd9b20ad532"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:30.329603Z","signature_b64":"D1IFCfD4LLkS0y0xRt1bUDt2azeWdcBT9DIiN+7rO2tK8Apjyiq8z/jvIlv6LtIC7aoBOiShPZE0MtHkKnbDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f9b7243a3bdabf728c7a3e437db5df42185f28c95a342a368126de666b7c9f4","last_reissued_at":"2026-05-17T23:41:30.328906Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:30.328906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An $L^p$-comparison, $p\\in (1,\\infty)$, on the finite differences of a discrete harmonic function at the boundary of a discrete box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.CA"],"primary_cat":"math.NA","authors_text":"Tuan Anh Nguyen","submitted_at":"2019-05-20T14:55:27Z","abstract_excerpt":"It is well-known that for a harmonic function $u$ defined on the unit ball of the $d$-dimensional Euclidean space, $d\\geq 2$, the tangential and normal component of the gradient $\\nabla u$ on the sphere are comparable by means of the $L^p$-norms, $p\\in(1,\\infty)$, up to multiplicative constants that depend only on $d,p$. This paper formulates and proves a discrete analogue of this result for discrete harmonic functions defined on a discrete box on the $d$-dimensional lattice with multiplicative constants that do not depend on the size of the box."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08151","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":"1905.08151","created_at":"2026-05-17T23:41:30.329008+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.08151v3","created_at":"2026-05-17T23:41:30.329008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08151","created_at":"2026-05-17T23:41:30.329008+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6NXEQ5DXWV7","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6NXEQ5DXWV7OKGH","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6NXEQ5D","created_at":"2026-05-18T12:33:27.125529+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/R6NXEQ5DXWV7OKGHUPSDPW256Q","json":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q.json","graph_json":"https://pith.science/api/pith-number/R6NXEQ5DXWV7OKGHUPSDPW256Q/graph.json","events_json":"https://pith.science/api/pith-number/R6NXEQ5DXWV7OKGHUPSDPW256Q/events.json","paper":"https://pith.science/paper/R6NXEQ5D"},"agent_actions":{"view_html":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q","download_json":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q.json","view_paper":"https://pith.science/paper/R6NXEQ5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.08151&json=true","fetch_graph":"https://pith.science/api/pith-number/R6NXEQ5DXWV7OKGHUPSDPW256Q/graph.json","fetch_events":"https://pith.science/api/pith-number/R6NXEQ5DXWV7OKGHUPSDPW256Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q/action/storage_attestation","attest_author":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q/action/author_attestation","sign_citation":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q/action/citation_signature","submit_replication":"https://pith.science/pith/R6NXEQ5DXWV7OKGHUPSDPW256Q/action/replication_record"}},"created_at":"2026-05-17T23:41:30.329008+00:00","updated_at":"2026-05-17T23:41:30.329008+00:00"}