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More precisely, we prove that if $ \\frac {8} {N + \\sqrt{ N^2 +16N }} < \\alpha \\le \\frac {4} {N} $, then small data give rise to global, scattering solutions in $H^1$."},"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":"1506.00294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-31T21:46:18Z","cross_cats_sorted":[],"title_canon_sha256":"03ac5529b84f5ca968b72e06dc91c7fdecc0e4db93349b190d3f3cb1f91bd9b3","abstract_canon_sha256":"992b693cd2f7805117c5afe1ed0a17db39330590d96981b2712ad86b6e5c34b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:41.787651Z","signature_b64":"zqE9qQxA1ERdOweHg7sE2mrs2F1v7kzk4F87xHio5vMu0Dq4NAtdfgpoddVmNAr1jLDjRKaa/Ei183LlmEa3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4806007a7da395cf25ee86f0b6160c9696b442848ba0e1b396ea1c8bf5671d3c","last_reissued_at":"2026-05-18T01:21:41.787220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:41.787220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Fujita-type blowup result and low energy scattering for a nonlinear Schr\\\"o\\-din\\-ger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fl\\'avio Dickstein, Fred B. 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