{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7Q2T36BMMVSYYVUZY3BMOPCUM4","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":"d3064d60f013a5f04ec3c8f7f23688e15a4c1de006fb579accd9f0e6581113ab","cross_cats_sorted":["math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T09:22:31Z","title_canon_sha256":"1bca0682dcb285865e5003a0207503987c913495acc4a16b8385e4c53cea8fd4"},"schema_version":"1.0","source":{"id":"2502.09103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.09103","created_at":"2026-07-05T10:13:52Z"},{"alias_kind":"arxiv_version","alias_value":"2502.09103v1","created_at":"2026-07-05T10:13:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09103","created_at":"2026-07-05T10:13:52Z"},{"alias_kind":"pith_short_12","alias_value":"7Q2T36BMMVSY","created_at":"2026-07-05T10:13:52Z"},{"alias_kind":"pith_short_16","alias_value":"7Q2T36BMMVSYYVUZ","created_at":"2026-07-05T10:13:52Z"},{"alias_kind":"pith_short_8","alias_value":"7Q2T36BM","created_at":"2026-07-05T10:13:52Z"}],"graph_snapshots":[{"event_id":"sha256:60fde50474d58c35a5308887775c2d962b5363c8315f690dff67fab6b93a01ce","target":"graph","created_at":"2026-07-05T10:13:52Z","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/2502.09103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with purely quadratic Hamiltonian. We show that for a globally Lipschitz-continuous terminal condition the rate is of order O($\\epsilon$ log $\\epsilon$), and we provide an example to show that this rate cannot be sharpened. This improves on the previously known rate of convergence O( $\\sqrt$ $\\epsilon$), which was widely believed to be optimal. Our proof combines techniques involving regularization by sup-convolution with entropy estimates for the fl","authors_text":"Louis-Pierre Chaintron (ENS-PSL), Samuel Daudin (UPCit\\'e)","cross_cats":["math.OC","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T09:22:31Z","title":"Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09103","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:eec2913c3431b98a0631780a73e0f76c5e067e0a16efb854602d27faa5c27711","target":"record","created_at":"2026-07-05T10:13:52Z","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":"d3064d60f013a5f04ec3c8f7f23688e15a4c1de006fb579accd9f0e6581113ab","cross_cats_sorted":["math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-13T09:22:31Z","title_canon_sha256":"1bca0682dcb285865e5003a0207503987c913495acc4a16b8385e4c53cea8fd4"},"schema_version":"1.0","source":{"id":"2502.09103","kind":"arxiv","version":1}},"canonical_sha256":"fc353df82c65658c5699c6c2c73c546727028cf29c6f14fdd63fbbf1b77539bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc353df82c65658c5699c6c2c73c546727028cf29c6f14fdd63fbbf1b77539bc","first_computed_at":"2026-07-05T10:13:52.538711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:52.538711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+kMfynJMxBDIOuK/B41nW5mYAqAEvGhl9+eFr5Unf4XggvcufTBzVs0nflipKs9BFuJ/0txVpJo1oxXz5ATDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:52.539155Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.09103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eec2913c3431b98a0631780a73e0f76c5e067e0a16efb854602d27faa5c27711","sha256:60fde50474d58c35a5308887775c2d962b5363c8315f690dff67fab6b93a01ce"],"state_sha256":"40360d37c62653e1de98e33fc221e98f66ad829dab2ce07e4f0757f72773d9c6"}