{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GTKXECZXU2N7FMTNWY3TSCNKN7","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":"b820b6d1005b9a2a0799e0b086b9c7916de7ff63b09d153e493d9ed85dd29991","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-24T08:06:30Z","title_canon_sha256":"01fbec560c6289bca2471925c9226a727b999f0440f0a676cbaa39c27725ec61"},"schema_version":"1.0","source":{"id":"2107.11554","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.11554","created_at":"2026-07-05T04:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"2107.11554v2","created_at":"2026-07-05T04:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.11554","created_at":"2026-07-05T04:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"GTKXECZXU2N7","created_at":"2026-07-05T04:56:11Z"},{"alias_kind":"pith_short_16","alias_value":"GTKXECZXU2N7FMTN","created_at":"2026-07-05T04:56:11Z"},{"alias_kind":"pith_short_8","alias_value":"GTKXECZX","created_at":"2026-07-05T04:56:11Z"}],"graph_snapshots":[{"event_id":"sha256:c79e8fe72d30e3830e326979c2addb9922cff3b8696017ea6b2ec051d67c0e90","target":"graph","created_at":"2026-07-05T04:56:11Z","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/2107.11554/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper deals with the generalized ergodic problem \\[ H(x,u(x),Du(x))=c, \\quad x\\in M, \\] \nwhere the unknown is a pair $(c,u)$ of a constant $c \\in \\mathbb{R}$ and a function $u$ on $M$ for which $u$ is a viscosity solution. We assume $H=H(x,u,p)$ satisfies Tonelli conditions in the argument $p\\in T^*_xM$ and the Lipschitz condition in the argument $u\\in\\R$.\n  For a given $c\\in \\R$, we first discuss necessary and sufficient conditions for the existence of viscosity solutions. Let $\\mathfrak{C}$ denote the set of all real numbers $c$'s for which the above equation admits viscosity solutions.","authors_text":"Jun Yan, Kaizhi Wang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-24T08:06:30Z","title":"Ergodic problems for contact Hamilton-Jacobi equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.11554","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":"sha256:3ea374de2326a8a81d69721d45d2aca5cc408a21da9907745a783136fe424a69","target":"record","created_at":"2026-07-05T04:56:11Z","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":"b820b6d1005b9a2a0799e0b086b9c7916de7ff63b09d153e493d9ed85dd29991","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-24T08:06:30Z","title_canon_sha256":"01fbec560c6289bca2471925c9226a727b999f0440f0a676cbaa39c27725ec61"},"schema_version":"1.0","source":{"id":"2107.11554","kind":"arxiv","version":2}},"canonical_sha256":"34d5720b37a69bf2b26db6373909aa6fe827200704622e450ba53a83436ca9b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34d5720b37a69bf2b26db6373909aa6fe827200704622e450ba53a83436ca9b5","first_computed_at":"2026-07-05T04:56:11.387710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:56:11.387710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PjKSgnfjBWyZS5tR7uO7sPVy9YTIzhFG/6zrRyyTD4k91y3Vl1aq61ixfAZ1asm4KuPJqrRdk14wbyo+65oMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:56:11.388184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.11554","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ea374de2326a8a81d69721d45d2aca5cc408a21da9907745a783136fe424a69","sha256:c79e8fe72d30e3830e326979c2addb9922cff3b8696017ea6b2ec051d67c0e90"],"state_sha256":"0053bcde661c6fba03b53dba11840e13889e579bcf32436036cb6356d0b766e7"}