{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GUJCHZXRNKSD7XS6WMKPD73F5M","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":"a8bac8439c797966930b036c137425927fbe5f4fbcf1c4d6d7a3dd84131ee448","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-21T05:13:30Z","title_canon_sha256":"21dd364a2f50615a66ae81065f023a06f2145ff4808f9a81f47e672a722d094b"},"schema_version":"1.0","source":{"id":"1503.06265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06265","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06265v1","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06265","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"GUJCHZXRNKSD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GUJCHZXRNKSD7XS6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GUJCHZXR","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:92c3db936e346d27e91adb657af2c9bc6ba4b7fbd9c16f5a72a00d89e6f940fb","target":"graph","created_at":"2026-05-18T02:20:38Z","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 investigate the Cauchy problem for a higher order shallow water type equation \\begin{eqnarray*} u_{t}-u_{txx}+\\partial_{x}^{2j+1}u-\\partial_{x}^{2j+3}u+3uu_{x}-2u_{x}u_{xx}-uu_{xxx}=0, \\end{eqnarray*} where $x\\in \\mathbf{T}=\\mathbf{R}/2\\pi$ and $j\\in N^{+}.$ Firstly, we prove that the Cauchy problem for the shallow water type equation is locally well-posed in $H^{s}(\\mathbf{T})$ with $s\\geq -\\frac{j-2}{2}$ for arbitrary initial data. By using the $I$-method, we prove that the Cauchy problem for the shallow water type equation is globally well-posed in $H^{s}(\\mathbf{T})$ with","authors_text":"Jianhua Huang, Wei Yan, Yongsheng Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-21T05:13:30Z","title":"The Cauchy problem for a higher order shallow water type equation on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06265","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":"sha256:47e500cd6a0111145ab7cd52b77f3a5c6cbc0cc8aba1daf52368f6ec5d6c8abd","target":"record","created_at":"2026-05-18T02:20:38Z","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":"a8bac8439c797966930b036c137425927fbe5f4fbcf1c4d6d7a3dd84131ee448","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-21T05:13:30Z","title_canon_sha256":"21dd364a2f50615a66ae81065f023a06f2145ff4808f9a81f47e672a722d094b"},"schema_version":"1.0","source":{"id":"1503.06265","kind":"arxiv","version":1}},"canonical_sha256":"351223e6f16aa43fde5eb314f1ff65eb1bb2341c3895686cc153927868eb3f8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"351223e6f16aa43fde5eb314f1ff65eb1bb2341c3895686cc153927868eb3f8a","first_computed_at":"2026-05-18T02:20:38.905270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:38.905270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DksfOgX+InTlC/IDn/kRO2/4YzUduxV6HNg5D8J1CgB/zgGOb0DNuudGedwhc4bYuMxJ6+b5WnNhCKXY9WGZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:38.906000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e500cd6a0111145ab7cd52b77f3a5c6cbc0cc8aba1daf52368f6ec5d6c8abd","sha256:92c3db936e346d27e91adb657af2c9bc6ba4b7fbd9c16f5a72a00d89e6f940fb"],"state_sha256":"f975dabe13fc3dc424d3a52f05a618e5a234916fd2f1c52796cbb55921d134f4"}