{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BONEIFF6HIHSVNACWI6C74KQAX","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":"1d8528e244b69ed339f51a50e9f41f5716dda689d6affcebcd1b4257664c3219","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-11T20:43:56Z","title_canon_sha256":"a8579236f043d6c1cf3274e71962a3f730c8b56e041e1f146b73db74bbad7da7"},"schema_version":"1.0","source":{"id":"1111.2850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2850","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2850v1","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2850","created_at":"2026-05-18T04:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"BONEIFF6HIHS","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BONEIFF6HIHSVNAC","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BONEIFF6","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:adea546f6abaae0aeffcf0d753d4ae09b51ee33c2994a581e63f3cc00e79c27d","target":"graph","created_at":"2026-05-18T04:08:24Z","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 prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\\partial_tu+\\Delta\\partial_xu+ u\\partial_xu=0$ in the Sobolev spaces $H^s(\\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\\R^3)$. The proof is based on a sharp maximal function estimate in time-weighted spaces.","authors_text":"Francis Ribaud (LAMA), St\\'ephane Vento (LAGA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-11T20:43:56Z","title":"Well-posedness results for the 3D Zakharov-Kuznetsov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2850","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:c23aa4a4ee44e746b30948d46a6b1bb4ec4006405b725fa469b9e0ca05188f3e","target":"record","created_at":"2026-05-18T04:08:24Z","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":"1d8528e244b69ed339f51a50e9f41f5716dda689d6affcebcd1b4257664c3219","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-11T20:43:56Z","title_canon_sha256":"a8579236f043d6c1cf3274e71962a3f730c8b56e041e1f146b73db74bbad7da7"},"schema_version":"1.0","source":{"id":"1111.2850","kind":"arxiv","version":1}},"canonical_sha256":"0b9a4414be3a0f2ab402b23c2ff15005f52d9ab77dcae3c927d9def4575bc372","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b9a4414be3a0f2ab402b23c2ff15005f52d9ab77dcae3c927d9def4575bc372","first_computed_at":"2026-05-18T04:08:24.880837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:24.880837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i1M7Ng4Olx6csZbpG73HEGgq6CN1XRxIrQbW2wz6EETNosBvhavd07iVRx8jnbbtMuXnmMdy+yTONOSMXQoiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:24.881373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c23aa4a4ee44e746b30948d46a6b1bb4ec4006405b725fa469b9e0ca05188f3e","sha256:adea546f6abaae0aeffcf0d753d4ae09b51ee33c2994a581e63f3cc00e79c27d"],"state_sha256":"ba6eef2c799f07da84fc8109801b633c0aaf6df1fa42f536043793fc86c53eb4"}