{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NM3AMQ5L7VHIKJZ63IS54RLWMQ","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":"81c38e27d289c7f5a0568ca88298aa416b1d154f9b952fced1433f54118af3df","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-24T11:32:04Z","title_canon_sha256":"4ed3d53bb69080464a14162afe81647bb56f207d630be05c2e3223ced5b0353d"},"schema_version":"1.0","source":{"id":"2510.21355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.21355","created_at":"2026-05-29T02:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"2510.21355v2","created_at":"2026-05-29T02:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.21355","created_at":"2026-05-29T02:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"NM3AMQ5L7VHI","created_at":"2026-05-29T02:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"NM3AMQ5L7VHIKJZ6","created_at":"2026-05-29T02:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"NM3AMQ5L","created_at":"2026-05-29T02:05:37Z"}],"graph_snapshots":[{"event_id":"sha256:145972e3c57b4c3b4353ebd969f670f2e4c4a62f6daef242ba7288165e86efe0","target":"graph","created_at":"2026-05-29T02:05:37Z","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/2510.21355/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper develops a fully discrete Fourier spectral Galerkin (FSG) method for the fractional Zakharov--Kuznetsov (fZK) equation posed on a two-dimensional periodic domain. The equation generalizes the classical ZK model by replacing the Laplacian with a fractional Laplacian of order \\(\\alpha\\in(0,2]\\), thereby covering the classical ZK equation \\(\\alpha=2\\), the higher-dimensional Benjamin--Ono--ZK equation \\(\\alpha=1\\), and weaker fractional-dispersion regimes \\(0<\\alpha<1\\). We first propose a semi-discrete FSG scheme in space that preserves the discrete analogues of mass, momentum, and Ha","authors_text":"Andreas Rupp, Mukul Dwivedi","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-24T11:32:04Z","title":"A numerical method for the fractional Zakharov-Kuznetsov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.21355","kind":"arxiv","version":2},"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":"sha256:382a40b4ad980af5be9be7675aef03a70e6875c9fb2c325c9bbb456658744a03","target":"record","created_at":"2026-05-29T02:05:37Z","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":"81c38e27d289c7f5a0568ca88298aa416b1d154f9b952fced1433f54118af3df","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2025-10-24T11:32:04Z","title_canon_sha256":"4ed3d53bb69080464a14162afe81647bb56f207d630be05c2e3223ced5b0353d"},"schema_version":"1.0","source":{"id":"2510.21355","kind":"arxiv","version":2}},"canonical_sha256":"6b360643abfd4e85273eda25de45766412fe54359897206bdba6e48f3644833a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b360643abfd4e85273eda25de45766412fe54359897206bdba6e48f3644833a","first_computed_at":"2026-05-29T02:05:37.340999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:37.340999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqT0SPl+tu4JoRnFiIFHmDsBzge4BJpTr9d7DtESLiEhKLRClrbuGxoGNsdE2C8x9jPVOe8bA98Q87uA04ZzBw==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:37.341582Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.21355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:382a40b4ad980af5be9be7675aef03a70e6875c9fb2c325c9bbb456658744a03","sha256:145972e3c57b4c3b4353ebd969f670f2e4c4a62f6daef242ba7288165e86efe0"],"state_sha256":"b7a37980e8ee813534751d7b0011830b67bb8c046f72f473d5f4dd23c08a82e7"}