{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YT4J65ZKGD7RS3F2S36Z45D4YR","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":"b004362693416e67ad8bbc0eb55dea13d8279d8d90202be13b57403f8e35cb7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-24T23:05:28Z","title_canon_sha256":"bebfa0892ec433ea43da742b84740c602fa901b88ffa2cf0abd70ba523f013fb"},"schema_version":"1.0","source":{"id":"1505.06497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06497","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06497v1","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06497","created_at":"2026-05-18T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"YT4J65ZKGD7R","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YT4J65ZKGD7RS3F2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YT4J65ZK","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:d9cc2ae3d203c3797349a7ea10b25396a572b3c77d1228d8ca28fdb44a7d85b7","target":"graph","created_at":"2026-05-18T02:03:44Z","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 Cauchy problem for the fourth order nonlinear Schr\\\"{o}dinger equation with derivative nonlinearity $(i\\partial _t + \\Delta ^2) u= \\pm \\partial (|u|^2u)$ on $\\mathbb{R} ^d$, $d \\ge 3$, with random initial data, where $\\partial$ is a first order derivative with respect to the spatial variable, for example a linear combination of $\\frac{\\partial}{\\partial x_1} , \\, \\dots , \\, \\frac{\\partial}{\\partial x_d}$ or $|\\nabla |= \\mathcal{F}^{-1}[|\\xi | \\mathcal{F}]$. We prove that almost sure local in time well-posedness, small data global in time well-posedness and scattering hold in $H","authors_text":"Hiroyuki Hirayama, Mamoru Okamoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-24T23:05:28Z","title":"Random data Cauchy theory for the fourth order nonlinear Schr\\\"{o}dinger equation with cubic nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06497","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:d78ee6b64e0d1a9a0d84216896115ddb9365d6039e7e7bb23a5104cc1b5bbe77","target":"record","created_at":"2026-05-18T02:03:44Z","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":"b004362693416e67ad8bbc0eb55dea13d8279d8d90202be13b57403f8e35cb7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-24T23:05:28Z","title_canon_sha256":"bebfa0892ec433ea43da742b84740c602fa901b88ffa2cf0abd70ba523f013fb"},"schema_version":"1.0","source":{"id":"1505.06497","kind":"arxiv","version":1}},"canonical_sha256":"c4f89f772a30ff196cba96fd9e747cc45a0b9e0bd66af6b33fbe9af38f7a3a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4f89f772a30ff196cba96fd9e747cc45a0b9e0bd66af6b33fbe9af38f7a3a4f","first_computed_at":"2026-05-18T02:03:44.842398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:44.842398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A2eMxhWet/My02Esbjt5Mcum7EIBNI2sYme+Olk6OilUcSJIS1qhVZgJopu8rLk4QHlSyn3AkPw5IedqzHG6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:44.843018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d78ee6b64e0d1a9a0d84216896115ddb9365d6039e7e7bb23a5104cc1b5bbe77","sha256:d9cc2ae3d203c3797349a7ea10b25396a572b3c77d1228d8ca28fdb44a7d85b7"],"state_sha256":"0d79cd65ea7dfb013fd3898f1054128de662478fa0cfdbe2b602b6c19399aace"}