{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2HRZQQJAZ7WT3B4URNVIF7UD47","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":"4e8fa1e6e41b3ba29bf371480092201006ab554622e178250700e1ed73f2f06b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-25T17:13:21Z","title_canon_sha256":"643812faf3f87ed0ea4dc301c1d3c3d14a592b57dd1af6c4ea4a5f3ec95a792d"},"schema_version":"1.0","source":{"id":"1710.09346","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09346","created_at":"2026-05-18T00:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09346v2","created_at":"2026-05-18T00:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09346","created_at":"2026-05-18T00:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"2HRZQQJAZ7WT","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2HRZQQJAZ7WT3B4U","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2HRZQQJA","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:785a2937f9453c95010a9d97c71fec9b3f6aa7e0a22b79befb8f260aac5242db","target":"graph","created_at":"2026-05-18T00:15:52Z","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 study nonlinear wave equations on $\\mathbb R^{2+1}$ with quadratic derivative nonlinearities, which include in particular nonlinearities exhibiting a null form structure, with random initial data in $H_x^1\\times L^2_x$. In contrast to the counterexamples of Zhou \\cite{Zhou} and Foschi-Klainerman \\cite{FK}, we obtain a uniform time interval $I$ on which the Picard iterates of all orders are almost surely bounded in $C_t(I ; \\dot H_x^1)$.","authors_text":"Andrea Nahmod, Dana Mendelson, Gigliola Staffilani, Magdalena Czubak, Sagun Chanillo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-25T17:13:21Z","title":"Almost sure boundedness of iterates for derivative nonlinear wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09346","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":"sha256:0bb2cc0ab4bfc082968fff6eec087306f87c7f305c76d9175be5f97110aae04d","target":"record","created_at":"2026-05-18T00:15:52Z","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":"4e8fa1e6e41b3ba29bf371480092201006ab554622e178250700e1ed73f2f06b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-25T17:13:21Z","title_canon_sha256":"643812faf3f87ed0ea4dc301c1d3c3d14a592b57dd1af6c4ea4a5f3ec95a792d"},"schema_version":"1.0","source":{"id":"1710.09346","kind":"arxiv","version":2}},"canonical_sha256":"d1e3984120cfed3d87948b6a82fe83e7ce272223923c18704af7f8f29db3cea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1e3984120cfed3d87948b6a82fe83e7ce272223923c18704af7f8f29db3cea9","first_computed_at":"2026-05-18T00:15:52.306474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:52.306474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgShQEUYQytuDkPZ/qjr0Gd3+Y0Ll+tcXxC2EQWxxn+zS0qFTSPqQLY7B0lmMpJ7e50ydLOloy3lZTdZ0z0GDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:52.307212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09346","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bb2cc0ab4bfc082968fff6eec087306f87c7f305c76d9175be5f97110aae04d","sha256:785a2937f9453c95010a9d97c71fec9b3f6aa7e0a22b79befb8f260aac5242db"],"state_sha256":"7b645d5d5d4f90d71400697b28d7a2ce91679424962b5c2849afe6bbbe5af588"}