{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CCSGSXKKGZZEVKGX5PRMJOLFB6","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":"ac169129952c01eb903c981c77e594a1b5a44f5be46f73376db7e4e63733f4ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-22T00:16:26Z","title_canon_sha256":"cbeecb3d067ca1c3d9873d0784e24e9f23563c37e09e3e3728be95885d512980"},"schema_version":"1.0","source":{"id":"1209.4943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4943","created_at":"2026-05-18T03:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4943v1","created_at":"2026-05-18T03:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4943","created_at":"2026-05-18T03:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"CCSGSXKKGZZE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CCSGSXKKGZZEVKGX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CCSGSXKK","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:e4809c5b12f5aba06352a906cf971009f12763228249fa2d5a4324dd438d3cdc","target":"graph","created_at":"2026-05-18T03:44:59Z","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 the question of global existence of small, smooth, and localized solutions of a certain fractional semilinear cubic NLS in one dimension, $$i\\partial_t u - \\Lambda u = c_0{|u|}^2 u + c_1 u^3 + c_2 u \\bar{u}^2 + c_3 \\bar{u}^3, \\qquad \\Lambda = \\Lambda(\\partial_x) = {|\\partial_x|}^(1/2)$$, where $c_0\\in\\mathbb{R}$ and $c_1,c_2,c_3\\in\\mathbb{C}$. This model is motivated by the two-dimensional water waves equations, which have a somewhat similar structure in the Eulerian formulation, in the case of irrotational flows. We show that one cannot expect linear scattering, even in this simpl","authors_text":"Alexandru D. Ionescu, Fabio Pusateri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-22T00:16:26Z","title":"Nonlinear fractional Schr\\\"odinger equations in one dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4943","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:c3f652992ddaed2d9f76545c747a2fd14b06474d8cb691cec2d97e20c920a285","target":"record","created_at":"2026-05-18T03:44:59Z","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":"ac169129952c01eb903c981c77e594a1b5a44f5be46f73376db7e4e63733f4ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-22T00:16:26Z","title_canon_sha256":"cbeecb3d067ca1c3d9873d0784e24e9f23563c37e09e3e3728be95885d512980"},"schema_version":"1.0","source":{"id":"1209.4943","kind":"arxiv","version":1}},"canonical_sha256":"10a4695d4a36724aa8d7ebe2c4b9650fa1ab19443da00d7f73b38f45de4b0b32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10a4695d4a36724aa8d7ebe2c4b9650fa1ab19443da00d7f73b38f45de4b0b32","first_computed_at":"2026-05-18T03:44:59.615958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:59.615958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LwacZ+1V9RrGDG3mBOLNVZ3kqtCL4lJ3bT6lu4rnGrbYhGlJw84liK4XS9DABFOEO0e7XTJkyGB2j9kN04zDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:59.616791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3f652992ddaed2d9f76545c747a2fd14b06474d8cb691cec2d97e20c920a285","sha256:e4809c5b12f5aba06352a906cf971009f12763228249fa2d5a4324dd438d3cdc"],"state_sha256":"01d7d9d3eefadec91c29aea3a3d1c7f751647f28a6da6be1c58e6a926327dda6"}