{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5VGYZ4QMBWCGB2YQUEPVMLUDZF","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":"a20aaa11684ce7607b81a3641bb3301e6287a037dbdf7411e64fb5f4d93ac297","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T16:53:53Z","title_canon_sha256":"9269bb2a5820862863fe37ca8ffc6e82954e8692ea744fc0812d2991f42201e0"},"schema_version":"1.0","source":{"id":"1509.08845","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08845","created_at":"2026-05-18T01:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08845v2","created_at":"2026-05-18T01:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08845","created_at":"2026-05-18T01:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"5VGYZ4QMBWCG","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5VGYZ4QMBWCGB2YQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5VGYZ4QM","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:3178dfffc4800f9c960b3d7e825eb5b71ea923be56f0f73dab49fff560f7611a","target":"graph","created_at":"2026-05-18T01:30:33Z","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":"We consider fractional NLS with focusing power-type nonlinearity $$i \\partial_t u = (-\\Delta)^s u - |u|^{2 \\sigma} u, \\quad (t,x) \\in \\mathbb{R} \\times \\mathbb{R}^N,$$ where $1/2< s < 1$ and $0 < \\sigma < \\infty$ for $s \\geq N/2$ and $0 < \\sigma \\leq 2s/(N-2s)$ for $s < N/2$. We prove a general criterion for blowup of radial solutions in $\\mathbb{R}^N$ with $N \\geq 2$ for $L^2$-supercritical and $L^2$-critical powers $\\sigma \\geq 2s/N$. In addition, we study the case of fractional NLS posed on a bounded star-shaped domain $\\Omega \\subset \\mathbb{R}^N$ in any dimension $N \\geq 1$ and subject to","authors_text":"Dominik Himmelsbach, Enno Lenzmann, Thomas Boulenger","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T16:53:53Z","title":"Blowup for fractional NLS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08845","kind":"arxiv","version":2},"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:f068d89b350070c1ec9a50f398ca2c32abde4038aa1f24d1e5705fb315f04796","target":"record","created_at":"2026-05-18T01:30:33Z","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":"a20aaa11684ce7607b81a3641bb3301e6287a037dbdf7411e64fb5f4d93ac297","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-29T16:53:53Z","title_canon_sha256":"9269bb2a5820862863fe37ca8ffc6e82954e8692ea744fc0812d2991f42201e0"},"schema_version":"1.0","source":{"id":"1509.08845","kind":"arxiv","version":2}},"canonical_sha256":"ed4d8cf20c0d8460eb10a11f562e83c95cc7dd6eff04667e8d0d6671db5e82c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed4d8cf20c0d8460eb10a11f562e83c95cc7dd6eff04667e8d0d6671db5e82c1","first_computed_at":"2026-05-18T01:30:33.910513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:33.910513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rM18MAZbWUfjMX5lfdwECjn7NEKYKUpa2K4JK3p5vuYpFZ/rJdwhpPgXpsfNQSXwglTbwFo8p1fIfwWIIGd+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:33.911177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08845","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f068d89b350070c1ec9a50f398ca2c32abde4038aa1f24d1e5705fb315f04796","sha256:3178dfffc4800f9c960b3d7e825eb5b71ea923be56f0f73dab49fff560f7611a"],"state_sha256":"138386da5e304dc59001be87cc4482c5ef96e8fc229eedab97db7bf38de8ef70"}