{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PXSAPUOXJ56QXBXO6YNGE3VX7A","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":"a91ae65a3c5ad183c1537415b35c9ae4d4a499f7d0d13751049ae9735f9d0e14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-10T23:43:58Z","title_canon_sha256":"c768de0f026dff41f43aa0277aa7c6ab32654a366d82a21cb1c867ce9e929ef0"},"schema_version":"1.0","source":{"id":"1605.03247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03247","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03247v1","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03247","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"PXSAPUOXJ56Q","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PXSAPUOXJ56QXBXO","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PXSAPUOX","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:b36371240f5337198cf1c83a5c634840617071fb42495cfd6aa3253f2adc7603","target":"graph","created_at":"2026-05-18T00:40:08Z","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 non-gauge-invariant cubic nonlinear Schr\\\"odinger equations in one space dimension. We show that initial data of size $\\varepsilon$ in a weighted Sobolev space lead to solutions with sharp $L_x^\\infty$ decay up to time $\\exp(C\\varepsilon^{-2})$. We also exhibit norm growth beyond this time for a specific choice of nonlinearity.","authors_text":"Fabio Pusateri, Jason Murphy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-10T23:43:58Z","title":"Almost global existence for cubic nonlinear Schr\\\"odinger equations in one space dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03247","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:c1a1011d61588595a297664425bef7ce049324c25dc055fc2e1c99991efd9546","target":"record","created_at":"2026-05-18T00:40:08Z","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":"a91ae65a3c5ad183c1537415b35c9ae4d4a499f7d0d13751049ae9735f9d0e14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-10T23:43:58Z","title_canon_sha256":"c768de0f026dff41f43aa0277aa7c6ab32654a366d82a21cb1c867ce9e929ef0"},"schema_version":"1.0","source":{"id":"1605.03247","kind":"arxiv","version":1}},"canonical_sha256":"7de407d1d74f7d0b86eef61a626eb7f8001408ef5ee6442f0a71c30d2b4c5a28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7de407d1d74f7d0b86eef61a626eb7f8001408ef5ee6442f0a71c30d2b4c5a28","first_computed_at":"2026-05-18T00:40:08.291852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:08.291852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvw1m/e9oL9/vseZUs5UIrkrJwAK1qadjoQd3sG8+wxD801TF34Yhp92spCN9tqHN/Nvork+lQHjiwnJg4rtDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:08.292245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1a1011d61588595a297664425bef7ce049324c25dc055fc2e1c99991efd9546","sha256:b36371240f5337198cf1c83a5c634840617071fb42495cfd6aa3253f2adc7603"],"state_sha256":"d27fa12ef556540af457fbccf7ffa92b39045344527a2ead1ca9897f84b0a3e5"}