{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LMYMLQ2OUEOJZ5QOXGQXPUUCGD","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":"67d7e8762b5eff1e8fdb794c11bcbfc907422f84b36a47621298b498780925ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T04:33:07Z","title_canon_sha256":"95a866eac39c270c7ccac8bcbb1f2618f533d135c44d0d55f29e22f8aeffa1e0"},"schema_version":"1.0","source":{"id":"2608.00438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00438","created_at":"2026-08-04T00:35:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00438v1","created_at":"2026-08-04T00:35:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00438","created_at":"2026-08-04T00:35:45Z"},{"alias_kind":"pith_short_12","alias_value":"LMYMLQ2OUEOJ","created_at":"2026-08-04T00:35:45Z"},{"alias_kind":"pith_short_16","alias_value":"LMYMLQ2OUEOJZ5QO","created_at":"2026-08-04T00:35:45Z"},{"alias_kind":"pith_short_8","alias_value":"LMYMLQ2O","created_at":"2026-08-04T00:35:45Z"}],"graph_snapshots":[{"event_id":"sha256:f84878b9481a4c32532dfd3e7fdcefa45ff43f727d4b1e8e5fff06365b3ea116","target":"graph","created_at":"2026-08-04T00:35:45Z","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/2608.00438/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the periodic homogenization of a class of viscous Hamilton--Jacobi equations with fast dependence on the unknown. This problem combines features of first-order Hamilton--Jacobi equations with \\(u^\\epsilon/\\epsilon\\)-periodic Hamiltonians and semilinear heat equations with rapidly oscillating positive potentials. In this paper, we prove qualitative homogenization results for $H(y,s,p)=F(s,p)+\\eta W(y,s,p)$ when $|\\eta|$ is sufficiently small, with the smallness threshold depending on the Lipschitz constant of the initial datum, and establish a large-time averaging result for a general ","authors_text":"Guyu Jin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T04:33:07Z","title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00438","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":"sha256:69efaf30b81f696442ac34b52c1d89e179fe9844e19a58c81b0b5c2a6ea8ec0a","target":"record","created_at":"2026-08-04T00:35:45Z","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":"67d7e8762b5eff1e8fdb794c11bcbfc907422f84b36a47621298b498780925ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-01T04:33:07Z","title_canon_sha256":"95a866eac39c270c7ccac8bcbb1f2618f533d135c44d0d55f29e22f8aeffa1e0"},"schema_version":"1.0","source":{"id":"2608.00438","kind":"arxiv","version":1}},"canonical_sha256":"5b30c5c34ea11c9cf60eb9a177d28230c57a9ab36f9c205e15751e93ab92a635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b30c5c34ea11c9cf60eb9a177d28230c57a9ab36f9c205e15751e93ab92a635","first_computed_at":"2026-08-04T00:35:45.827174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T00:35:45.827174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YzWLhWRy/S26QfUdZkEZtbYUGZM5JpNo9xwsBSRrigL9JdwJYFHMZvvtfDv5qjoa12+NXTHVguRnoxY7ciKeAw==","signature_status":"signed_v1","signed_at":"2026-08-04T00:35:45.828604Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69efaf30b81f696442ac34b52c1d89e179fe9844e19a58c81b0b5c2a6ea8ec0a","sha256:f84878b9481a4c32532dfd3e7fdcefa45ff43f727d4b1e8e5fff06365b3ea116"],"state_sha256":"f3d64915ab56e2aa05c28855de94e4c9ec82529f51f1d2d7da0f258d2dea61ea"}