{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SPKZRSLNRILUATTP2XSYAILVEI","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":"507d96fa8b3e58d3f7f04c9c6e1c8b8a228d37b2955a05d81896be3a57fec96e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-20T15:37:28Z","title_canon_sha256":"c4d8b6b37cd3338cdaf64f5e4c715b4d404837d8494f3fce1d9a37dd029f3ca9"},"schema_version":"1.0","source":{"id":"2606.22103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22103","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22103v1","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22103","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_12","alias_value":"SPKZRSLNRILU","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_16","alias_value":"SPKZRSLNRILUATTP","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_8","alias_value":"SPKZRSLN","created_at":"2026-06-23T02:13:28Z"}],"graph_snapshots":[{"event_id":"sha256:5c71faafa732597ff2c34a781c00982c002ee9d9a3e3b0afeca9283d0758732b","target":"graph","created_at":"2026-06-23T02:13:28Z","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/2606.22103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a homogenization problem for first-order Hamilton-Jacobi equations in the Wasserstein space with a convex Hamiltonian. We show that the solution $U^\\varepsilon$, which is the value function of a mean field control problem, converges uniformly as $\\varepsilon \\to 0$ to the solution of a limiting Hamilton-Jacobi equation whose Hamiltonian is obtained through a suitable cell problem. Furthermore, we establish quantitative rates of convergence. Under general assumptions with multiscale dependence, we prove that the rate of convergence is $O(\\sqrt{\\varepsilon})$. When the Hamiltonian depen","authors_text":"Antonios Zitridis, Ibrahim Ekren, Yuxi Han, Zhiyan Ding","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-20T15:37:28Z","title":"Quantitative homogenization of convex Hamilton-Jacobi equations in the Wasserstein space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22103","kind":"arxiv","version":1},"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":"sha256:0b06ba1c130cb1ceaa99d25ea23a3bc3dcd1d9c9d4647da7d00be212438a3a80","target":"record","created_at":"2026-06-23T02:13:28Z","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":"507d96fa8b3e58d3f7f04c9c6e1c8b8a228d37b2955a05d81896be3a57fec96e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-20T15:37:28Z","title_canon_sha256":"c4d8b6b37cd3338cdaf64f5e4c715b4d404837d8494f3fce1d9a37dd029f3ca9"},"schema_version":"1.0","source":{"id":"2606.22103","kind":"arxiv","version":1}},"canonical_sha256":"93d598c96d8a17404e6fd5e580217522155cf706652d3d250db75bc07487e8c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93d598c96d8a17404e6fd5e580217522155cf706652d3d250db75bc07487e8c0","first_computed_at":"2026-06-23T02:13:28.310451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:28.310451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0SJGQ+r/7IfCYp+82H9DCoEC4pIoYL7Qlygfw1Y3amyjhZy8S8E0Zmif25QcJ0LJ/IEwsckK1zW5dcnH/Aa4DQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:28.310812Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b06ba1c130cb1ceaa99d25ea23a3bc3dcd1d9c9d4647da7d00be212438a3a80","sha256:5c71faafa732597ff2c34a781c00982c002ee9d9a3e3b0afeca9283d0758732b"],"state_sha256":"c2e7fbd9c16e9b276856b0bd0c3f8557d217e3fce631e284be340a6473e4af2c"}