{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y4E5K2CBR3LO2KJI7AGBVIYYFP","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":"4a00e56ff7f32519aa57578dd71816206612e3721dcdcff98ea437c472415d70","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-03T14:20:40Z","title_canon_sha256":"b9c0373cce2533c25f89ea71043f049803e48fd16ee632a68f337eea8e718178"},"schema_version":"1.0","source":{"id":"1106.0648","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0648","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0648v3","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0648","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y4E5K2CBR3LO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y4E5K2CBR3LO2KJI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y4E5K2CB","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:f02abfe3c972b5c94579662c3538d9f9dba34ae610c12fbff7d00943f9cc3de0","target":"graph","created_at":"2026-05-18T04:15:59Z","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":"Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation (mKdV) found by Grosse are shown to be globally $H^1$-stable. Stability in the one-kink case was previously established by Zhidkov, and Merle-Vega. The proof uses transformations linking the mKdV equation with focusing, Gardner-like equations, where stability and asymptotic stability in the energy space are known. We generalize our results by considering the existence, uniqueness and the dynamics of generalized multi-kinks of defocusing, non-integrable gKdV equations, showing the inelastic character of the 4-kink colli","authors_text":"Claudio Mu\\~noz","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-03T14:20:40Z","title":"The Gardner equation and the stability of multi-kink solutions of the mKdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0648","kind":"arxiv","version":3},"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":"sha256:698acc4938b23b1ccb8b228b8f8806dd665e9ab1738522dd9dbdc4bc870275f3","target":"record","created_at":"2026-05-18T04:15:59Z","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":"4a00e56ff7f32519aa57578dd71816206612e3721dcdcff98ea437c472415d70","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-03T14:20:40Z","title_canon_sha256":"b9c0373cce2533c25f89ea71043f049803e48fd16ee632a68f337eea8e718178"},"schema_version":"1.0","source":{"id":"1106.0648","kind":"arxiv","version":3}},"canonical_sha256":"c709d568418ed6ed2928f80c1aa3182bfb24362807dd808763e02d4648bfd2a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c709d568418ed6ed2928f80c1aa3182bfb24362807dd808763e02d4648bfd2a9","first_computed_at":"2026-05-18T04:15:59.246044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:59.246044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r7ikPiggCcbiK6RMYixu+nttFG7r+7nLGVaPHe6YgbZ1jIncVu+4NGLWj2qzbAgzbuzHTROmD72VQHPhNtEkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:59.246629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0648","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:698acc4938b23b1ccb8b228b8f8806dd665e9ab1738522dd9dbdc4bc870275f3","sha256:f02abfe3c972b5c94579662c3538d9f9dba34ae610c12fbff7d00943f9cc3de0"],"state_sha256":"581d8b6646212abe2eab81de61cc0997773d2ef009cfdbd7b1ff3ccb88ed01d1"}