{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BZKGZTYKCITMGLB675VY42VU7L","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":"f5cefb999478dbd5a412162f9c4b3b40218b8c30352a006139c12bbb84808d72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-29T17:54:49Z","title_canon_sha256":"1f458e56d973fd39508489bd83df0a5c98b6e5284f80dc1acc722482d8d77bb0"},"schema_version":"1.0","source":{"id":"1911.13265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.13265","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1911.13265v1","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.13265","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"BZKGZTYKCITM","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"pith_short_16","alias_value":"BZKGZTYKCITMGLB6","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"pith_short_8","alias_value":"BZKGZTYK","created_at":"2026-07-05T00:22:53Z"}],"graph_snapshots":[{"event_id":"sha256:ab51fe2b21810326f8078a2b0614ac2b046c85c10c69a8c1b8ab6f65bad5ffe0","target":"graph","created_at":"2026-07-05T00:22:53Z","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/1911.13265/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with the Cauchy problem of the modified Zakharov-Kuznetsov equation on $\\mathbb{R}^d$. If $d=2$, we prove the sharp estimate which implies local in time well-posedness in the Sobolev space $H^s(\\mathbb{R}^2)$ for $s \\geq 1/4$. If $d \\geq 3$, by employing $U^p$ and $V^p$ spaces, we establish the small data global well-posedness in the scaling critical Sobolev space $H^{s_c}(\\mathbb{R}^d)$ where $s_c = d/2-1$.","authors_text":"Shinya Kinoshita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-29T17:54:49Z","title":"Well-posedness for the Cauchy problem of the modified Zakharov-Kuznetsov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.13265","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":"sha256:99b014456399cda7e3a174020fa0b09325eb30aa26fcddadf74d5984fd90bcfd","target":"record","created_at":"2026-07-05T00:22:53Z","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":"f5cefb999478dbd5a412162f9c4b3b40218b8c30352a006139c12bbb84808d72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-29T17:54:49Z","title_canon_sha256":"1f458e56d973fd39508489bd83df0a5c98b6e5284f80dc1acc722482d8d77bb0"},"schema_version":"1.0","source":{"id":"1911.13265","kind":"arxiv","version":1}},"canonical_sha256":"0e546ccf0a1226c32c3eff6b8e6ab4fae786cc1cabccd00762319028ce28ffdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e546ccf0a1226c32c3eff6b8e6ab4fae786cc1cabccd00762319028ce28ffdb","first_computed_at":"2026-07-05T00:22:53.526252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:53.526252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EiHPf7m6xZYg94aLOLOT5L4bR4UiZsyKqM+EXrCwvQ13SDJ57RC8Rng/vlGhZlqv6gUvaMIvmtEf1jXVp67tBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:53.526644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.13265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99b014456399cda7e3a174020fa0b09325eb30aa26fcddadf74d5984fd90bcfd","sha256:ab51fe2b21810326f8078a2b0614ac2b046c85c10c69a8c1b8ab6f65bad5ffe0"],"state_sha256":"c78e3573331d4fa6d16e9387212052e2b65d0b1a6e911eba64b998bfb80c1001"}