{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BERP4MAB2IDVWO35U47NPW2WUB","short_pith_number":"pith:BERP4MAB","canonical_record":{"source":{"id":"2112.06896","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2021-12-13T18:53:12Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"7f3a3c7ef2c53807c5d91b938d2b091f5d9ac102f230ceb9c453e266ceafa6e7","abstract_canon_sha256":"c40a740a5ec3a187af8e0b4741302366596acc99c6f3fce652c3e9e817526223"},"schema_version":"1.0"},"canonical_sha256":"0922fe3001d2075b3b7da73ed7db56a0566808ad693b212b1a7f64210d515ac6","source":{"kind":"arxiv","id":"2112.06896","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.06896","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"2112.06896v2","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06896","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"BERP4MAB2IDV","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"pith_short_16","alias_value":"BERP4MAB2IDVWO35","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"pith_short_8","alias_value":"BERP4MAB","created_at":"2026-07-05T04:36:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BERP4MAB2IDVWO35U47NPW2WUB","target":"record","payload":{"canonical_record":{"source":{"id":"2112.06896","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2021-12-13T18:53:12Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"7f3a3c7ef2c53807c5d91b938d2b091f5d9ac102f230ceb9c453e266ceafa6e7","abstract_canon_sha256":"c40a740a5ec3a187af8e0b4741302366596acc99c6f3fce652c3e9e817526223"},"schema_version":"1.0"},"canonical_sha256":"0922fe3001d2075b3b7da73ed7db56a0566808ad693b212b1a7f64210d515ac6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:36:21.305183Z","signature_b64":"EVTmf5jexedJsUdIs5//03Ml1vqS2PKVNBKN8jpac8n3coUmd6QfuCq7j4I0MI2PnDRC1plofmN6CCOImJBkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0922fe3001d2075b3b7da73ed7db56a0566808ad693b212b1a7f64210d515ac6","last_reissued_at":"2026-07-05T04:36:21.304726Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:36:21.304726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.06896","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5FmMdStFxSF3iBaVlJ3Np3U2+Xm0sm3M+fyWlhJGI0ZOcnML7LnKJDevmGDvXWsd8oRAxyKNCarkR/ZFUf3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:53:31.851534Z"},"content_sha256":"1a95a7a237275c0e001a297948fe2652255d4f8c334a276509e6ba03a3b10323","schema_version":"1.0","event_id":"sha256:1a95a7a237275c0e001a297948fe2652255d4f8c334a276509e6ba03a3b10323"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BERP4MAB2IDVWO35U47NPW2WUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal convergence rate for periodic homogenization of convex Hamilton-Jacobi equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Hung V. Tran, Yifeng Yu","submitted_at":"2021-12-13T18:53:12Z","abstract_excerpt":"In this paper, we show that the rate of convergence in periodic homogenization of convex Hamilton-Jacobi equations is always $O(\\varepsilon)$, which is optimal. This is a natural extension of a result concerning stable norms in metric geometry [4] that is essentially equivalent to the homogenization of convex static Hamilton-Jacobi equations. Another extremely interesting question in this direction is whether the $O(\\varepsilon)$ rate holds in the nonconvex setting. We present a special nonconvex example with $O(\\varepsilon)$ convergence rate, which relies on identifying the shape of the effec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06896","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.06896/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fe6anEETE+iPrOkxa0H3CsF5Z3DH8S/0iq7W3P+LodoXY3FPI2RJVNq1a1NMQWZPTJumU9GtcSaWHelBxULLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:53:31.852064Z"},"content_sha256":"c0a466ef27734584a3e4c279c5d08eb78a9283c31b9b1fea96d89847d5820e42","schema_version":"1.0","event_id":"sha256:c0a466ef27734584a3e4c279c5d08eb78a9283c31b9b1fea96d89847d5820e42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BERP4MAB2IDVWO35U47NPW2WUB/bundle.json","state_url":"https://pith.science/pith/BERP4MAB2IDVWO35U47NPW2WUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BERP4MAB2IDVWO35U47NPW2WUB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T04:53:31Z","links":{"resolver":"https://pith.science/pith/BERP4MAB2IDVWO35U47NPW2WUB","bundle":"https://pith.science/pith/BERP4MAB2IDVWO35U47NPW2WUB/bundle.json","state":"https://pith.science/pith/BERP4MAB2IDVWO35U47NPW2WUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BERP4MAB2IDVWO35U47NPW2WUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BERP4MAB2IDVWO35U47NPW2WUB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c40a740a5ec3a187af8e0b4741302366596acc99c6f3fce652c3e9e817526223","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2021-12-13T18:53:12Z","title_canon_sha256":"7f3a3c7ef2c53807c5d91b938d2b091f5d9ac102f230ceb9c453e266ceafa6e7"},"schema_version":"1.0","source":{"id":"2112.06896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.06896","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"2112.06896v2","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06896","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"BERP4MAB2IDV","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"pith_short_16","alias_value":"BERP4MAB2IDVWO35","created_at":"2026-07-05T04:36:21Z"},{"alias_kind":"pith_short_8","alias_value":"BERP4MAB","created_at":"2026-07-05T04:36:21Z"}],"graph_snapshots":[{"event_id":"sha256:c0a466ef27734584a3e4c279c5d08eb78a9283c31b9b1fea96d89847d5820e42","target":"graph","created_at":"2026-07-05T04:36:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.06896/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show that the rate of convergence in periodic homogenization of convex Hamilton-Jacobi equations is always $O(\\varepsilon)$, which is optimal. This is a natural extension of a result concerning stable norms in metric geometry [4] that is essentially equivalent to the homogenization of convex static Hamilton-Jacobi equations. Another extremely interesting question in this direction is whether the $O(\\varepsilon)$ rate holds in the nonconvex setting. We present a special nonconvex example with $O(\\varepsilon)$ convergence rate, which relies on identifying the shape of the effec","authors_text":"Hung V. Tran, Yifeng Yu","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2021-12-13T18:53:12Z","title":"Optimal convergence rate for periodic homogenization of convex Hamilton-Jacobi equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06896","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1a95a7a237275c0e001a297948fe2652255d4f8c334a276509e6ba03a3b10323","target":"record","created_at":"2026-07-05T04:36:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c40a740a5ec3a187af8e0b4741302366596acc99c6f3fce652c3e9e817526223","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2021-12-13T18:53:12Z","title_canon_sha256":"7f3a3c7ef2c53807c5d91b938d2b091f5d9ac102f230ceb9c453e266ceafa6e7"},"schema_version":"1.0","source":{"id":"2112.06896","kind":"arxiv","version":2}},"canonical_sha256":"0922fe3001d2075b3b7da73ed7db56a0566808ad693b212b1a7f64210d515ac6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0922fe3001d2075b3b7da73ed7db56a0566808ad693b212b1a7f64210d515ac6","first_computed_at":"2026-07-05T04:36:21.304726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:36:21.304726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EVTmf5jexedJsUdIs5//03Ml1vqS2PKVNBKN8jpac8n3coUmd6QfuCq7j4I0MI2PnDRC1plofmN6CCOImJBkAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:36:21.305183Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.06896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a95a7a237275c0e001a297948fe2652255d4f8c334a276509e6ba03a3b10323","sha256:c0a466ef27734584a3e4c279c5d08eb78a9283c31b9b1fea96d89847d5820e42"],"state_sha256":"a208a0a409dd0b3434830d7aa5b6ece60d3856da864f84b2aa8d74351c085f13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TrAFkDfHpzOne/7FL8pZimZ3s0SflbUO0gYuBbMTq12IZlOthKfDKmf6Tc065Wc9qFZQQR9JhaNVIfm4djdVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T04:53:31.855946Z","bundle_sha256":"56951ca38b0e77f2f8a61c1737e24766e8e8b86e03ea97e8a14a692e6f2d1b04"}}