{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XDOKJ655V6FU5JCXJ6GDCONRLW","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":"129d31ee4389c8ac06c04c8664f9b948bd334e8fb2a239c5152bb9725c8bf516","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-20T17:35:21Z","title_canon_sha256":"13784a73a6d498ec2619a79d24d6f0fdf9212f11c4e2b93a5c8f3ec17a50f383"},"schema_version":"1.0","source":{"id":"2506.17179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17179","created_at":"2026-07-05T11:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17179v1","created_at":"2026-07-05T11:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17179","created_at":"2026-07-05T11:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"XDOKJ655V6FU","created_at":"2026-07-05T11:24:57Z"},{"alias_kind":"pith_short_16","alias_value":"XDOKJ655V6FU5JCX","created_at":"2026-07-05T11:24:57Z"},{"alias_kind":"pith_short_8","alias_value":"XDOKJ655","created_at":"2026-07-05T11:24:57Z"}],"graph_snapshots":[{"event_id":"sha256:fbde9416dab697a4e7f635cb27110f0ef4894c686ed82162e7c0c6b795e64e20","target":"graph","created_at":"2026-07-05T11:24:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.17179/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the modified Zakharov-Kuznetsov equation in dimension $2$ : \\[ \\partial_t u + \\partial_x \\left( \\Delta u + u^3 \\right) = 0 \\] where $u : (t, (x, y)) \\in \\mathbb{R} \\times \\mathbb{R}^2 \\mapsto u(t, x, y) \\in \\mathbb{R}$ and $\\Delta = \\partial_x^2 + \\partial_y^2$ is the full Laplacian. We prove that solutions for small and localized initial data scatter for large time. Our proof relies on the method of space-time resonances.","authors_text":"Philippe Anjolras","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-20T17:35:21Z","title":"Scattering of the 2D modified Zakharov-Kuznetsov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17179","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":"sha256:6048d8bffebf3c7f69aaee727f9a07fc8de09da91ac77a4bceb329ad981ba6a4","target":"record","created_at":"2026-07-05T11:24:57Z","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":"129d31ee4389c8ac06c04c8664f9b948bd334e8fb2a239c5152bb9725c8bf516","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-20T17:35:21Z","title_canon_sha256":"13784a73a6d498ec2619a79d24d6f0fdf9212f11c4e2b93a5c8f3ec17a50f383"},"schema_version":"1.0","source":{"id":"2506.17179","kind":"arxiv","version":1}},"canonical_sha256":"b8dca4fbbdaf8b4ea4574f8c3139b15d9d05f149498c495dc4f307bd75e307a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8dca4fbbdaf8b4ea4574f8c3139b15d9d05f149498c495dc4f307bd75e307a6","first_computed_at":"2026-07-05T11:24:57.441360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:57.441360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"905+edxbaVbvWk/Ed9xiombO0W0/b6CiA3aBEvK8DXeq50SYItHkcXbTvZ3VT7mF/F43h4/NIxbpKIMvlst3Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:57.441964Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.17179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6048d8bffebf3c7f69aaee727f9a07fc8de09da91ac77a4bceb329ad981ba6a4","sha256:fbde9416dab697a4e7f635cb27110f0ef4894c686ed82162e7c0c6b795e64e20"],"state_sha256":"460844c36a5c0ae278eb8ff568f2c4decccc0eaec6f29895df515b6719d3d78e"}