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In the focusing case ($\\mu=1$), we show that if the initial data $u_0$ belongs to $H^1(\\R)$ and satisfies $E(u_0)^{s_k} M(u_0)^{1-s_k} < E(Q)^{s_k} M(Q)^{1-s_k}$, $E(u_0)\\geq0$, and $\\|\\partial_x u_0\\|_{L^2}^{s_k}\\|u_0\\|_{L^2}^{1-s_k} < \\|\\partial_x Q\\|_{L^2}^{s_k}\\|Q\\|_{L^2}^{1-s_k}$, where $M(u)$ and $E(u)$ are the mass and energy, then the corresponding solution is global in $H^1(\\R)$. Here, $s_k=\\frac{(k-4)}{2k}$ and $Q$ ","authors_text":"Ademir Pastor, Felipe Linares, Luiz Gustavo Farah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-16T18:10:09Z","title":"The supercritical generalized KdV equation: Global well-posedness in the energy space and below"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3234","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":"sha256:2f981055dc978d3e1c3de9547c9e33986f9c989497fde5ccdd6ed02d3b8f2556","target":"record","created_at":"2026-05-18T03:57:00Z","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":"64cbbc10218b23484ddc04c8341d44dfe1a176ecf71402fafa57ee4f04f277ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-16T18:10:09Z","title_canon_sha256":"a29b5f4d8897abc51bba6497b06db1d9430225542da7cbac4a854ceb88255a77"},"schema_version":"1.0","source":{"id":"1009.3234","kind":"arxiv","version":1}},"canonical_sha256":"cef0f10d89e33166272afb7334789ab733af73a813984c62f6ecdd5b4802e459","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cef0f10d89e33166272afb7334789ab733af73a813984c62f6ecdd5b4802e459","first_computed_at":"2026-05-18T03:57:00.946033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:00.946033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CW+rap/cvVzehweVHn4sI8NQr6gGi/fBExB2+Rh4c87lLRZYGy6+hj2i/9oVoiIgb2B0Uf7XSdxbiNLNGgqFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:00.946770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f981055dc978d3e1c3de9547c9e33986f9c989497fde5ccdd6ed02d3b8f2556","sha256:bec793581428092bf70f55e853141c0dd30c1aa313d46c5a3f59ee039172e963"],"state_sha256":"6d998444d04c5c56e0d2c6a61be88fcda10a4bf543780649230fec10ae222e51"}