{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WKFDGSJDLQTLXADFKDE4LYMZ5W","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":"5b6a631eda4dc35c34888c10619ee4369d54dc35255eeb464b11ed2b98718d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-01T02:18:16Z","title_canon_sha256":"72f52c2d4c4140c152d9e44509e203b2aa956c3910e4b512bd7d89ec91f0590a"},"schema_version":"1.0","source":{"id":"1903.00127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00127","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00127v1","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00127","created_at":"2026-05-17T23:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"WKFDGSJDLQTL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WKFDGSJDLQTLXADF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WKFDGSJD","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c8c5e00de6c8aff34e078fc3a22bb730d7e3d7c616c6a203400827f3da502145","target":"graph","created_at":"2026-05-17T23:52:20Z","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":"In this paper, we study the following nonlinear Schr\\\"odinger equation \\begin{eqnarray}\\label{maineq0} \\textbf{i}u_{t}-u_{xx}+V*u+\\epsilon f(x)|u|^4u=0,\\ x\\in\\mathbb{T}=\\mathbb{R}/2\\pi\\mathbb{Z}, \\end{eqnarray} where $V*$ is the Fourier multiplier defined by $\\widehat{(V* u})_n=V_{n}\\widehat{u}_n, V_n\\in[-1,1]$ and $f(x)$ is Gevrey smooth. It is shown that for $0\\leq|\\epsilon|\\ll1$, there is some $(V_n)_{n\\in\\mathbb{Z}}$ such that, the equation admits a time almost periodic solution (i.e., full dimensional KAM torus) in the Gevrey space. This extends results of Bourgain \\cite{BJFA2005} and Con","authors_text":"Hongzi Cong, Lufang Mi, Yuan Wu, Yunfeng Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-01T02:18:16Z","title":"On the existence of full dimensional KAM torus for nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00127","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":"sha256:2da6aff4de0cdac6152ed418f66dceaed5ae2dfeab5759a042f6a5be27060495","target":"record","created_at":"2026-05-17T23:52:20Z","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":"5b6a631eda4dc35c34888c10619ee4369d54dc35255eeb464b11ed2b98718d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-01T02:18:16Z","title_canon_sha256":"72f52c2d4c4140c152d9e44509e203b2aa956c3910e4b512bd7d89ec91f0590a"},"schema_version":"1.0","source":{"id":"1903.00127","kind":"arxiv","version":1}},"canonical_sha256":"b28a3349235c26bb806550c9c5e199ed8ff7b0d81293cb8e8a152f440be8ba17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b28a3349235c26bb806550c9c5e199ed8ff7b0d81293cb8e8a152f440be8ba17","first_computed_at":"2026-05-17T23:52:20.840744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:20.840744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZKJvUvQ4DA67m1s8i6woOv3NEbSnWX8F5Dv6Cw8HyhB9FOM6kZvyydHeUNzFn7TgYp7O+lZZ50YASfEJe4oDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:20.841344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2da6aff4de0cdac6152ed418f66dceaed5ae2dfeab5759a042f6a5be27060495","sha256:c8c5e00de6c8aff34e078fc3a22bb730d7e3d7c616c6a203400827f3da502145"],"state_sha256":"17fd3c6a7647926e0fd2e4480d21e8e03b23d87d870796bcd6fe3ba27fcbb49f"}