{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LZJWYRVGP77YKJUGKI256UBSHJ","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":"1028d85e6dea1cba3a45fcd101cefe57acc38b65b461d14d1d6672271c1e507d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-13T17:56:23Z","title_canon_sha256":"04fc922b843efa9f7cd8b6081eb978cbdbde5bb454d5c176fd6193d000c4d448"},"schema_version":"1.0","source":{"id":"1902.05034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05034","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05034v1","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05034","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"LZJWYRVGP77Y","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LZJWYRVGP77YKJUG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LZJWYRVG","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:7d044f8d8842a80269391b2ff7eeffd76f3c704515bd490387b45bf3f89b9dc7","target":"graph","created_at":"2026-05-17T23:54:03Z","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"},"paper":{"abstract_excerpt":"We study a generalized ergodic problem (E), which is a Hamilton-Jacobi equation of contact type, in the flat $n$-dimensional torus. We first obtain existence of solutions to this problem under quite general assumptions. Various examples are presented and analyzed to show that (E) does not have unique solutions in general. We then study uniqueness structures of solutions to (E) in the convex setting by using the nonlinear adjoint method.","authors_text":"Hiroyoshi Mitake, Hung V. Tran, Wenjia Jing","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-13T17:56:23Z","title":"Generalized ergodic problems: existence and uniqueness structures of solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05034","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:cbe0473d380c1f7e29b24ad96540c69aaea5f972c4768b6db319da27bd28ab9f","target":"record","created_at":"2026-05-17T23:54:03Z","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":"1028d85e6dea1cba3a45fcd101cefe57acc38b65b461d14d1d6672271c1e507d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-13T17:56:23Z","title_canon_sha256":"04fc922b843efa9f7cd8b6081eb978cbdbde5bb454d5c176fd6193d000c4d448"},"schema_version":"1.0","source":{"id":"1902.05034","kind":"arxiv","version":1}},"canonical_sha256":"5e536c46a67fff8526865235df50323a4dd263bd0a3fbba1f8e47500b45d2e09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e536c46a67fff8526865235df50323a4dd263bd0a3fbba1f8e47500b45d2e09","first_computed_at":"2026-05-17T23:54:03.572385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:03.572385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9fR5wV0ERAGeG625BEa48VJvMdsSrxnw7mHntrFBbXDo4KmcoUEPT0Xa1nRrCk2Lp0uHFJjzCdGA/gi9s4vDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:03.572797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbe0473d380c1f7e29b24ad96540c69aaea5f972c4768b6db319da27bd28ab9f","sha256:7d044f8d8842a80269391b2ff7eeffd76f3c704515bd490387b45bf3f89b9dc7"],"state_sha256":"0b8caa8dc2d9ebf0918c1b4f055afa7354938b4d1dbab43005b9e2dba8d4d656"}