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We prove both time and space sharp asymptotics for $S$ close to the blow up time. 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) - ","authors_text":"Vianney Combet, Yvan Martel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-10T20:59:34Z","title":"Sharp asymptotics for the minimal mass blow up solution of critical gKdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03519","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:e196b0bab9a926377c8734c845cb7bdf85eaa3d870ee82d2158952631517a037","target":"record","created_at":"2026-05-18T01:20:59Z","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":"ffc2938307609c11a9dca26b28136e1c567ddcd3eee84b3bd9319d544f7f0b1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-10T20:59:34Z","title_canon_sha256":"cb969e60ab9fbece5ea98d17a25a678c134524df3c9f37997d755d6fbad65a84"},"schema_version":"1.0","source":{"id":"1602.03519","kind":"arxiv","version":1}},"canonical_sha256":"13fa2b8de16f16284449524754e57a19f4f87863eab293fea3c867d40d960e0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13fa2b8de16f16284449524754e57a19f4f87863eab293fea3c867d40d960e0e","first_computed_at":"2026-05-18T01:20:59.748368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:59.748368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vi/jSO4B+EhSV6Rsb9z58KcnkIyqEQ9ovwEpXARgHGds0PwVdGIFv1KDSiEFEJY48kWkKb8xkGa71YZwxx/oDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:59.749021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e196b0bab9a926377c8734c845cb7bdf85eaa3d870ee82d2158952631517a037","sha256:6ce31776c2d9f56af3ed60a10fa98cf68ff16a16eed1cab56ba379b5086ef04a"],"state_sha256":"bce4c2c103d4d978bf2066d128f636857e4f695e759d687d12c03982408f2097"}