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Let $Q$ be the unique ground state of (gKdV), satisfying $Q\"+Q^5=Q$.\n  First, we show that there exist universal smooth profiles $Q_k\\in\\mathcal{S}(\\mathbb{R})$ (with $Q_0=Q$) and a constant $c_0\\in\\mathbb{R}$ such that, fixing the blow up time at $t=0$ and appropriate scaling and translation parameters, $S$ satisfies, for any $m\\geqslant 0$, \\[ \\partial_x^m S(t) - "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.03519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-10T20:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"cb969e60ab9fbece5ea98d17a25a678c134524df3c9f37997d755d6fbad65a84","abstract_canon_sha256":"ffc2938307609c11a9dca26b28136e1c567ddcd3eee84b3bd9319d544f7f0b1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:59.749021Z","signature_b64":"Vi/jSO4B+EhSV6Rsb9z58KcnkIyqEQ9ovwEpXARgHGds0PwVdGIFv1KDSiEFEJY48kWkKb8xkGa71YZwxx/oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13fa2b8de16f16284449524754e57a19f4f87863eab293fea3c867d40d960e0e","last_reissued_at":"2026-05-18T01:20:59.748368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:59.748368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp asymptotics for the minimal mass blow up solution of critical gKdV equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vianney Combet, Yvan Martel","submitted_at":"2016-02-10T20:59:34Z","abstract_excerpt":"Let $S$ be a minimal mass blow up solution of the critical generalized KdV equation as constructed by Martel, Merle and Rapha\\\"el in arXiv:1204.4624. 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