{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TTI45ALWQHR6AGPYZAUJGJCWPQ","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":"74ab3849897af17f81ca9e648e0f5c18bd99ee37d67ba97404ad6d8f25491cb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-06T14:55:06Z","title_canon_sha256":"6e05263e20c67e4ab714590cf2a703267ce0640f409201732455f4c914bcefad"},"schema_version":"1.0","source":{"id":"1809.02027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02027","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02027v1","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02027","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"TTI45ALWQHR6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TTI45ALWQHR6AGPY","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TTI45ALW","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:e13e837a07d5cf4108040b47a59e9476cdaf6afa33382a1e646f600e31ceaab7","target":"graph","created_at":"2026-05-18T00:06:21Z","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 consider the Cauchy problem associated with the Zakharov-Kuznetsov equation, posed on $\\mathbb{T}^2$. We prove the local well-posedness for given data in $H^s(\\mathbb{T}^2)$ whenever $s>5/3$. More importantly, we prove that this equation is of quasi-linear type for initial data in any Sobolev space on the torus, in sharp contrast with its semi-linear character in the $\\mathbb{R}^2$ and $\\mathbb{R}\\times \\mathbb{T}$ settings.","authors_text":"Felipe Linares, Mahendra Panthee, Nikolay Tzvetkov, Tristan Robert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-06T14:55:06Z","title":"On the periodic Zakharov-Kuznetsov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02027","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:dab7b71217ada4781fb6cb7dda3511aebb38b6106162f18ec212639dfd24af41","target":"record","created_at":"2026-05-18T00:06:21Z","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":"74ab3849897af17f81ca9e648e0f5c18bd99ee37d67ba97404ad6d8f25491cb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-06T14:55:06Z","title_canon_sha256":"6e05263e20c67e4ab714590cf2a703267ce0640f409201732455f4c914bcefad"},"schema_version":"1.0","source":{"id":"1809.02027","kind":"arxiv","version":1}},"canonical_sha256":"9cd1ce817681e3e019f8c8289324567c02789c0834fc9371e00e46e352309820","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cd1ce817681e3e019f8c8289324567c02789c0834fc9371e00e46e352309820","first_computed_at":"2026-05-18T00:06:21.503203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:21.503203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"URiqemGfp6LvnZoWVfuB14neKq4SJhVLUbK0pcpDjX9nd5Kpv5uBwQaZS/cw36vIOlJiiTSnLe0uTSE/TAK0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:21.503620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dab7b71217ada4781fb6cb7dda3511aebb38b6106162f18ec212639dfd24af41","sha256:e13e837a07d5cf4108040b47a59e9476cdaf6afa33382a1e646f600e31ceaab7"],"state_sha256":"8684429548631960b560860149fd108a9af3158e527e80dca1194b875940c073"}