{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZYLNRNPNQXOCO5DJAMHW4EPXSD","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":"db478ad488edf52a58cbef63750678aedb6de260d42ef891c857761495a688db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-17T08:08:18Z","title_canon_sha256":"4336cf684fe2b714456bfb376ae7a1ba9415ef9a19304929ccf05a0ca51cf6c4"},"schema_version":"1.0","source":{"id":"1602.05331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05331","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05331v1","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05331","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZYLNRNPNQXOC","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZYLNRNPNQXOCO5DJ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZYLNRNPN","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:7cac7add009cecf6a3e55f2da686234c658c3d984a1e0be4a7b2c0a7fed0f495","target":"graph","created_at":"2026-05-18T01:20:28Z","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 article, we prove existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg-de Vries (gKdV) equation in the scale critical ^L^r space. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to ^L^r-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schr\"odinger equation.","authors_text":"Jun-ichi Segata, Satoshi Masaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-17T08:08:18Z","title":"Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05331","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:effbb5a53d9f29aac2263734bb423632ea4b0300615a16fe8188a3fe70cdd111","target":"record","created_at":"2026-05-18T01:20:28Z","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":"db478ad488edf52a58cbef63750678aedb6de260d42ef891c857761495a688db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-17T08:08:18Z","title_canon_sha256":"4336cf684fe2b714456bfb376ae7a1ba9415ef9a19304929ccf05a0ca51cf6c4"},"schema_version":"1.0","source":{"id":"1602.05331","kind":"arxiv","version":1}},"canonical_sha256":"ce16d8b5ed85dc277469030f6e11f790f358dcd91dc249bab970dccf1231e5f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce16d8b5ed85dc277469030f6e11f790f358dcd91dc249bab970dccf1231e5f3","first_computed_at":"2026-05-18T01:20:28.542212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:28.542212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYr9gSSwn0KQIK/PCFUxuJvUDAkRK1qTizNIoujWeQNluU1oXf0tYHSWFaxiRJd+Tq5jzx8lPEg1XEEo/iUXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:28.542834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:effbb5a53d9f29aac2263734bb423632ea4b0300615a16fe8188a3fe70cdd111","sha256:7cac7add009cecf6a3e55f2da686234c658c3d984a1e0be4a7b2c0a7fed0f495"],"state_sha256":"dbedac27980dc91bc56bf0748c1c5ae575091ed5bc55ca8330d297bb618ca995"}