{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BZKGZTYKCITMGLB675VY42VU7L","short_pith_number":"pith:BZKGZTYK","schema_version":"1.0","canonical_sha256":"0e546ccf0a1226c32c3eff6b8e6ab4fae786cc1cabccd00762319028ce28ffdb","source":{"kind":"arxiv","id":"1911.13265","version":1},"attestation_state":"computed","paper":{"title":"Well-posedness for the Cauchy problem of the modified Zakharov-Kuznetsov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shinya Kinoshita","submitted_at":"2019-11-29T17:54:49Z","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 $s_c = d/2-1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1911.13265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-29T17:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"1f458e56d973fd39508489bd83df0a5c98b6e5284f80dc1acc722482d8d77bb0","abstract_canon_sha256":"f5cefb999478dbd5a412162f9c4b3b40218b8c30352a006139c12bbb84808d72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:53.526644Z","signature_b64":"EiHPf7m6xZYg94aLOLOT5L4bR4UiZsyKqM+EXrCwvQ13SDJ57RC8Rng/vlGhZlqv6gUvaMIvmtEf1jXVp67tBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e546ccf0a1226c32c3eff6b8e6ab4fae786cc1cabccd00762319028ce28ffdb","last_reissued_at":"2026-07-05T00:22:53.526252Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:53.526252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Well-posedness for the Cauchy problem of the modified Zakharov-Kuznetsov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shinya Kinoshita","submitted_at":"2019-11-29T17:54:49Z","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 $s_c = d/2-1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.13265","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.13265/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1911.13265","created_at":"2026-07-05T00:22:53.526328+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.13265v1","created_at":"2026-07-05T00:22:53.526328+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.13265","created_at":"2026-07-05T00:22:53.526328+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZKGZTYKCITM","created_at":"2026-07-05T00:22:53.526328+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZKGZTYKCITMGLB6","created_at":"2026-07-05T00:22:53.526328+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZKGZTYK","created_at":"2026-07-05T00:22:53.526328+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2501.09157","citing_title":"On the minimal Blow-up rate for the 2D generalized Zakharov- Kuznetsov model","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L","json":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L.json","graph_json":"https://pith.science/api/pith-number/BZKGZTYKCITMGLB675VY42VU7L/graph.json","events_json":"https://pith.science/api/pith-number/BZKGZTYKCITMGLB675VY42VU7L/events.json","paper":"https://pith.science/paper/BZKGZTYK"},"agent_actions":{"view_html":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L","download_json":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L.json","view_paper":"https://pith.science/paper/BZKGZTYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.13265&json=true","fetch_graph":"https://pith.science/api/pith-number/BZKGZTYKCITMGLB675VY42VU7L/graph.json","fetch_events":"https://pith.science/api/pith-number/BZKGZTYKCITMGLB675VY42VU7L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L/action/storage_attestation","attest_author":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L/action/author_attestation","sign_citation":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L/action/citation_signature","submit_replication":"https://pith.science/pith/BZKGZTYKCITMGLB675VY42VU7L/action/replication_record"}},"created_at":"2026-07-05T00:22:53.526328+00:00","updated_at":"2026-07-05T00:22:53.526328+00:00"}