{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:C7Z3KEOYIVPXVBY37GMRD2AJIN","short_pith_number":"pith:C7Z3KEOY","canonical_record":{"source":{"id":"2412.20027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-28T05:15:59Z","cross_cats_sorted":["hep-th","math-ph","math.MP","physics.flu-dyn"],"title_canon_sha256":"1625f56ca607e90f11ab7ab201ccf257793f631e679e7ff8697130e8de734aa5","abstract_canon_sha256":"4fb666a8699d92c7a112e9414171aca5247bc317bfadc575478eee2303f67c9c"},"schema_version":"1.0"},"canonical_sha256":"17f3b511d8455f7a871bf99911e8094354ef3f9507e5d2e6469530b791236879","source":{"kind":"arxiv","id":"2412.20027","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20027","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20027v2","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20027","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"C7Z3KEOYIVPX","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"pith_short_16","alias_value":"C7Z3KEOYIVPXVBY3","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"pith_short_8","alias_value":"C7Z3KEOY","created_at":"2026-07-05T11:29:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:C7Z3KEOYIVPXVBY37GMRD2AJIN","target":"record","payload":{"canonical_record":{"source":{"id":"2412.20027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-28T05:15:59Z","cross_cats_sorted":["hep-th","math-ph","math.MP","physics.flu-dyn"],"title_canon_sha256":"1625f56ca607e90f11ab7ab201ccf257793f631e679e7ff8697130e8de734aa5","abstract_canon_sha256":"4fb666a8699d92c7a112e9414171aca5247bc317bfadc575478eee2303f67c9c"},"schema_version":"1.0"},"canonical_sha256":"17f3b511d8455f7a871bf99911e8094354ef3f9507e5d2e6469530b791236879","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:53.505128Z","signature_b64":"rfDM0qeSpC0bXedSRTqEOwIaTlI9R3LYqDkXJBMYWjty+E55FihOb7ozjPAJxgnyNTtQVopnfsgt67IY8aJRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f3b511d8455f7a871bf99911e8094354ef3f9507e5d2e6469530b791236879","last_reissued_at":"2026-07-05T11:29:53.504712Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:53.504712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.20027","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LvQmCyzCNokvILF6TTD7g6RSmKacjbbEhXxvnakOQL7F05fJqnIe9pdiDkUA2d/l1c3ffKqSy8cGapumOpZWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:40:36.786006Z"},"content_sha256":"150d32b533bc4c57165ddaab5e7377b490e0910cbfcdec620216240c1cc07ccc","schema_version":"1.0","event_id":"sha256:150d32b533bc4c57165ddaab5e7377b490e0910cbfcdec620216240c1cc07ccc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:C7Z3KEOYIVPXVBY37GMRD2AJIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inelastic Scattering, Emergent Interactions of Solitons in the Zakharov-Kuznetsov Equation through Conservative and non-Conservative Physics-Informed Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","physics.flu-dyn"],"primary_cat":"nlin.SI","authors_text":"A. Nakamula, K. Obuse, K. Shimasaki, K. Toda, N. Sawado, Y. Shimazaki, Y. Suzuki","submitted_at":"2024-12-28T05:15:59Z","abstract_excerpt":"The Zakharov-Kuznetsov equation, originally a three dimensional mathematical model of plasma with a uniform magnetic field, is a direct extension of the KdV equation into higher dimensions and is a typical quasi-integrable system. Physics-Informed Neural Networks (PINNs) are used to study the collision of soliton solutions in the 2+1 dimensional Zakharov-Kuznetsov equation. PINNs are able to successfully solve the equations in the forward process, and the solutions are obtained using a mesh-free approach and automatic differentiation, taking into account conservation laws. In the inverse proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20027","kind":"arxiv","version":2},"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/2412.20027/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLlW+IfMOdjS3e2E+1B2rEiHXOeEjAemxTcOTJJq4kPmfsfO49MEh1oMj3UtPt1SyKkVS6iJ40+suU3MWEZ+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:40:36.786508Z"},"content_sha256":"2de555e18200c4c387537b0c08b9a28cd408ab219ff9bcff9c8bacf6567bb5a2","schema_version":"1.0","event_id":"sha256:2de555e18200c4c387537b0c08b9a28cd408ab219ff9bcff9c8bacf6567bb5a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN/bundle.json","state_url":"https://pith.science/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T12:40:36Z","links":{"resolver":"https://pith.science/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN","bundle":"https://pith.science/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN/bundle.json","state":"https://pith.science/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C7Z3KEOYIVPXVBY37GMRD2AJIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:C7Z3KEOYIVPXVBY37GMRD2AJIN","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":"4fb666a8699d92c7a112e9414171aca5247bc317bfadc575478eee2303f67c9c","cross_cats_sorted":["hep-th","math-ph","math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-28T05:15:59Z","title_canon_sha256":"1625f56ca607e90f11ab7ab201ccf257793f631e679e7ff8697130e8de734aa5"},"schema_version":"1.0","source":{"id":"2412.20027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20027","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20027v2","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20027","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"C7Z3KEOYIVPX","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"pith_short_16","alias_value":"C7Z3KEOYIVPXVBY3","created_at":"2026-07-05T11:29:53Z"},{"alias_kind":"pith_short_8","alias_value":"C7Z3KEOY","created_at":"2026-07-05T11:29:53Z"}],"graph_snapshots":[{"event_id":"sha256:2de555e18200c4c387537b0c08b9a28cd408ab219ff9bcff9c8bacf6567bb5a2","target":"graph","created_at":"2026-07-05T11:29:53Z","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/2412.20027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Zakharov-Kuznetsov equation, originally a three dimensional mathematical model of plasma with a uniform magnetic field, is a direct extension of the KdV equation into higher dimensions and is a typical quasi-integrable system. Physics-Informed Neural Networks (PINNs) are used to study the collision of soliton solutions in the 2+1 dimensional Zakharov-Kuznetsov equation. PINNs are able to successfully solve the equations in the forward process, and the solutions are obtained using a mesh-free approach and automatic differentiation, taking into account conservation laws. In the inverse proce","authors_text":"A. Nakamula, K. Obuse, K. Shimasaki, K. Toda, N. Sawado, Y. Shimazaki, Y. Suzuki","cross_cats":["hep-th","math-ph","math.MP","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-28T05:15:59Z","title":"Inelastic Scattering, Emergent Interactions of Solitons in the Zakharov-Kuznetsov Equation through Conservative and non-Conservative Physics-Informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20027","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":"sha256:150d32b533bc4c57165ddaab5e7377b490e0910cbfcdec620216240c1cc07ccc","target":"record","created_at":"2026-07-05T11:29:53Z","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":"4fb666a8699d92c7a112e9414171aca5247bc317bfadc575478eee2303f67c9c","cross_cats_sorted":["hep-th","math-ph","math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-28T05:15:59Z","title_canon_sha256":"1625f56ca607e90f11ab7ab201ccf257793f631e679e7ff8697130e8de734aa5"},"schema_version":"1.0","source":{"id":"2412.20027","kind":"arxiv","version":2}},"canonical_sha256":"17f3b511d8455f7a871bf99911e8094354ef3f9507e5d2e6469530b791236879","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17f3b511d8455f7a871bf99911e8094354ef3f9507e5d2e6469530b791236879","first_computed_at":"2026-07-05T11:29:53.504712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:53.504712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rfDM0qeSpC0bXedSRTqEOwIaTlI9R3LYqDkXJBMYWjty+E55FihOb7ozjPAJxgnyNTtQVopnfsgt67IY8aJRDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:53.505128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.20027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:150d32b533bc4c57165ddaab5e7377b490e0910cbfcdec620216240c1cc07ccc","sha256:2de555e18200c4c387537b0c08b9a28cd408ab219ff9bcff9c8bacf6567bb5a2"],"state_sha256":"b9ef28897a1bfaf2c8c4e056d45fb86f16a28150d58fbba6212fe95e8dffb1ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cP2REjWYiO1VZbtJjeG4VXHnu+4A47C3/PBd8HiJ74/NWVhBTOFpSJhnPjO0v1h7kO0nuPQcyu9tHa57nRjZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:40:36.790525Z","bundle_sha256":"09505f34655ca82a919db7ff8c317571e82aadcc1d2ed6c41748bde15e419cc2"}}