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Here, $u^\\epsilon$ and $u$ are viscosity solutions to the oscillatory Hamilton-Jacobi equation and its effective equation \\begin{equation*} {\\rm (C)_\\epsilon} \\qquad \\begin{cases} u_t^\\epsilon+H\\left(\\frac{x}{\\epsilon},Du^\\epsilon\\right)=0 \\qquad &\\text{in} \\ \\mathbb{R}^n \\times (0,\\infty), u^\\epsilon(x,0)=g(x) \\qquad &\\text{on} \\ \\mathbb{R}^n, \\end{cases} \\end{equation*} and \\begin{equation*} {\\rm (C)} \\qquad \\begin{cases} u_t+\\overline{H}\\left(Du\\right)=0 \\q"},"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":"1801.00391","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-01T04:19:55Z","cross_cats_sorted":["math.DS","math.OC"],"title_canon_sha256":"7688dbde340ba448fe919f660a11db0c90258db626fb4cad54ab029bf2a2b641","abstract_canon_sha256":"9528f3034a26a22f591e09da1f83827d73e8ffe44e6b31eaef62af065bd194f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:24.578328Z","signature_b64":"QyQOGoY2Pqx81+MweICmbOn0sApjCsOuj9i0eaE+YRPzrd1HBkl4+kqdziMkOPURydtek1CejzYLvtxzxnSiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"250f6ae24b435c1c7ab282195aef1376540b699e8dcb2c4054634c21aeacdbc0","last_reissued_at":"2026-05-17T23:52:24.577864Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:24.577864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"math.AP","authors_text":"Hiroyoshi Mitake, Hung V. Tran, Yifeng Yu","submitted_at":"2018-01-01T04:19:55Z","abstract_excerpt":"We study the rate of convergence of $u^\\epsilon$, as $\\epsilon \\to 0+$, to $u$ in periodic homogenization of Hamilton-Jacobi equations. Here, $u^\\epsilon$ and $u$ are viscosity solutions to the oscillatory Hamilton-Jacobi equation and its effective equation \\begin{equation*} {\\rm (C)_\\epsilon} \\qquad \\begin{cases} u_t^\\epsilon+H\\left(\\frac{x}{\\epsilon},Du^\\epsilon\\right)=0 \\qquad &\\text{in} \\ \\mathbb{R}^n \\times (0,\\infty), u^\\epsilon(x,0)=g(x) \\qquad &\\text{on} \\ \\mathbb{R}^n, \\end{cases} \\end{equation*} and \\begin{equation*} {\\rm (C)} \\qquad \\begin{cases} u_t+\\overline{H}\\left(Du\\right)=0 \\q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00391","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":"1801.00391","created_at":"2026-05-17T23:52:24.577933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00391v3","created_at":"2026-05-17T23:52:24.577933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00391","created_at":"2026-05-17T23:52:24.577933+00:00"},{"alias_kind":"pith_short_12","alias_value":"EUHWVYSLINOB","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EUHWVYSLINOBY6VS","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EUHWVYSL","created_at":"2026-05-18T12:32:22.470017+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/EUHWVYSLINOBY6VSQIMVV3YTOZ","json":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ.json","graph_json":"https://pith.science/api/pith-number/EUHWVYSLINOBY6VSQIMVV3YTOZ/graph.json","events_json":"https://pith.science/api/pith-number/EUHWVYSLINOBY6VSQIMVV3YTOZ/events.json","paper":"https://pith.science/paper/EUHWVYSL"},"agent_actions":{"view_html":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ","download_json":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ.json","view_paper":"https://pith.science/paper/EUHWVYSL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00391&json=true","fetch_graph":"https://pith.science/api/pith-number/EUHWVYSLINOBY6VSQIMVV3YTOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EUHWVYSLINOBY6VSQIMVV3YTOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ/action/storage_attestation","attest_author":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ/action/author_attestation","sign_citation":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ/action/citation_signature","submit_replication":"https://pith.science/pith/EUHWVYSLINOBY6VSQIMVV3YTOZ/action/replication_record"}},"created_at":"2026-05-17T23:52:24.577933+00:00","updated_at":"2026-05-17T23:52:24.577933+00:00"}