{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CY5NDQMOCREVUEAPSZ3JKAQAFY","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":"d85f3533c508ad5facdf749f286ca45e124a625d99d82e2ddd12773468c52df3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-04-29T03:30:05Z","title_canon_sha256":"f073b55d5b61ae8a1305e6da7b359f64402f406e154998a97205493266e3f2ed"},"schema_version":"1.0","source":{"id":"1804.10863","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10863","created_at":"2026-07-05T00:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10863v1","created_at":"2026-07-05T00:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10863","created_at":"2026-07-05T00:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"CY5NDQMOCREV","created_at":"2026-07-05T00:01:24Z"},{"alias_kind":"pith_short_16","alias_value":"CY5NDQMOCREVUEAP","created_at":"2026-07-05T00:01:24Z"},{"alias_kind":"pith_short_8","alias_value":"CY5NDQMO","created_at":"2026-07-05T00:01:24Z"}],"graph_snapshots":[{"event_id":"sha256:f96b2e630bbdd39d61b049a140215aa4187bd933eb4b0e843a16fb7a72497ee7","target":"graph","created_at":"2026-07-05T00:01:24Z","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/1804.10863/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) \n  \\[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_x(x,t)=0,\\]\n  which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal mKdV equation. In contrast with the classical mKdV equation, we find some new a","authors_text":"Engui Fan, Fengjing He, Jian Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-04-29T03:30:05Z","title":"Long-time asymptotics for the Nonlocal mKdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10863","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":"sha256:71b6bb5f24aa02483bd43f55eeb87da737c197ef72a491ad5e68e603e825eea6","target":"record","created_at":"2026-07-05T00:01:24Z","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":"d85f3533c508ad5facdf749f286ca45e124a625d99d82e2ddd12773468c52df3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-04-29T03:30:05Z","title_canon_sha256":"f073b55d5b61ae8a1305e6da7b359f64402f406e154998a97205493266e3f2ed"},"schema_version":"1.0","source":{"id":"1804.10863","kind":"arxiv","version":1}},"canonical_sha256":"163ad1c18e14495a100f96769502002e3f6435523b1f35cac9f2dbd76bf58d90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"163ad1c18e14495a100f96769502002e3f6435523b1f35cac9f2dbd76bf58d90","first_computed_at":"2026-07-05T00:01:24.190748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:01:24.190748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CwksbZfQaxHIXO1T96B/jMMoIiSGEZXdRnlx/KavCHFAR6p0pWmZE7Hr+Qo55foEEk06yNzKi2UPe/hGgA8TBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:01:24.191191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10863","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71b6bb5f24aa02483bd43f55eeb87da737c197ef72a491ad5e68e603e825eea6","sha256:f96b2e630bbdd39d61b049a140215aa4187bd933eb4b0e843a16fb7a72497ee7"],"state_sha256":"08c56f2fc50de9e89f380e737f169d09ed0a3ae9efc4e5fced4eacf6cd1e7885"}