{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:45D4WP7CIKM2DSKW35KNBOJ6DD","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":"bd692695d9d8325078db589487855fc1bae8d588553922083c1ee1a173a57225","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-30T08:05:20Z","title_canon_sha256":"0a70116f6de5bcbc205b5cf26b3b4405a44de059d27d735f411b4f6b31f6cafb"},"schema_version":"1.0","source":{"id":"1801.00099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00099","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00099v1","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00099","created_at":"2026-05-18T00:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"45D4WP7CIKM2","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"45D4WP7CIKM2DSKW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"45D4WP7C","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:5fd7b8dab492615d5e4ad23198e5ac564eae10bddddd2b3f768f9bd12ce88581","target":"graph","created_at":"2026-05-18T00:26:59Z","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":"Motivated by water-wave problems, in this paper we consider a class of nonlinear dispersive PDEs in 2D with cubic nonlinearities, whose dispersion relations are radial and have vanishing Guassian curvature on a circle. For such a model we identify certain null structures for the cubic nonlinearity, which suffice in order to guarantee global scattering solutions for the small data problem. Our null structures in the power-type nonlinearity are weak, and only eliminate the worst nonlinear interaction. Such null structures arise naturally in some water-wave problems.","authors_text":"Daniel Tataru, Yuqiu Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-30T08:05:20Z","title":"Null structures and degenerate dispersion relations in two space dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00099","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":"sha256:175337118f9d0922a02135876609357b80a7f2c6411dbc797f4aa9804d580dcc","target":"record","created_at":"2026-05-18T00:26:59Z","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":"bd692695d9d8325078db589487855fc1bae8d588553922083c1ee1a173a57225","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-30T08:05:20Z","title_canon_sha256":"0a70116f6de5bcbc205b5cf26b3b4405a44de059d27d735f411b4f6b31f6cafb"},"schema_version":"1.0","source":{"id":"1801.00099","kind":"arxiv","version":1}},"canonical_sha256":"e747cb3fe24299a1c956df54d0b93e18c5b9d3d634e5091d143cb43e12fc630a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e747cb3fe24299a1c956df54d0b93e18c5b9d3d634e5091d143cb43e12fc630a","first_computed_at":"2026-05-18T00:26:59.446198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:59.446198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"caQ3gCYi41ywqRPdiD/QFNPp+UY2Y0b4pFqKjToLxmjsz6GUa5GTG6sfzwQgjE54303WzWMVw8YmKwEqiDQGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:59.446751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:175337118f9d0922a02135876609357b80a7f2c6411dbc797f4aa9804d580dcc","sha256:5fd7b8dab492615d5e4ad23198e5ac564eae10bddddd2b3f768f9bd12ce88581"],"state_sha256":"98f4f6eb49902fe7602f477b24cfb43d9fdc8ff9ae380203575a4f7385add06b"}