{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SAAOD7KU5SY25T4BUNXK47CSJ3","short_pith_number":"pith:SAAOD7KU","canonical_record":{"source":{"id":"1902.05688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-15T05:24:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"3ad7581f7bf4d59b86d147390642b936c2f26e7fd014198c527d3a2fcc3391e5","abstract_canon_sha256":"4abcbf860cbee3ab83f15b538518e95a76cf2c3a36e8ea30a08f05b2065dd66f"},"schema_version":"1.0"},"canonical_sha256":"9000e1fd54ecb1aecf81a36eae7c524ee0164b291e8ddb5b45584875485271af","source":{"kind":"arxiv","id":"1902.05688","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05688","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05688v1","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05688","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"SAAOD7KU5SY2","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"pith_short_16","alias_value":"SAAOD7KU5SY25T4B","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"pith_short_8","alias_value":"SAAOD7KU","created_at":"2026-06-04T20:13:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SAAOD7KU5SY25T4BUNXK47CSJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1902.05688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-15T05:24:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"3ad7581f7bf4d59b86d147390642b936c2f26e7fd014198c527d3a2fcc3391e5","abstract_canon_sha256":"4abcbf860cbee3ab83f15b538518e95a76cf2c3a36e8ea30a08f05b2065dd66f"},"schema_version":"1.0"},"canonical_sha256":"9000e1fd54ecb1aecf81a36eae7c524ee0164b291e8ddb5b45584875485271af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:54.140098Z","signature_b64":"rRnGWtB2FA7NIxuKjHIwr1R88uocPdKAtVmg8jImu1Bfo8WYu0mNNvzK3yJavan6sR5d9uPIZpkMTuA3kWXQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9000e1fd54ecb1aecf81a36eae7c524ee0164b291e8ddb5b45584875485271af","last_reissued_at":"2026-06-04T20:13:54.139589Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:54.139589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.05688","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T20:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWSJbelKKVCWgra1s/XalCcEFCf0brRdIptQqfehediDgzjkuZa61oTYmmd0AfgaXPCJNl6XoAd2x1sNOk89DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:58:24.010054Z"},"content_sha256":"c015554939fd3fa6cac0a33c64899bbe75199b1bebad1fc2e38039dc81b43a06","schema_version":"1.0","event_id":"sha256:c015554939fd3fa6cac0a33c64899bbe75199b1bebad1fc2e38039dc81b43a06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SAAOD7KU5SY25T4BUNXK47CSJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Liwei Xu, Maojun Li, Yongping Cheng","submitted_at":"2019-02-15T05:24:22Z","abstract_excerpt":"In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05688","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/1902.05688/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":"2026-06-04T20:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6UDXbsoGJWKV1MNRX8K6ITQRH55USjA8/6AlLlfXZhQ4dbyKV+BNiNOIc46XmAb1Sw+5oVg4z3sFtRZSL+QQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:58:24.010445Z"},"content_sha256":"90b851a50a4485b76fa3ad630c03769fa3eee3b4298799e903298a8662e12db5","schema_version":"1.0","event_id":"sha256:90b851a50a4485b76fa3ad630c03769fa3eee3b4298799e903298a8662e12db5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAAOD7KU5SY25T4BUNXK47CSJ3/bundle.json","state_url":"https://pith.science/pith/SAAOD7KU5SY25T4BUNXK47CSJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAAOD7KU5SY25T4BUNXK47CSJ3/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":"2026-06-10T19:58:24Z","links":{"resolver":"https://pith.science/pith/SAAOD7KU5SY25T4BUNXK47CSJ3","bundle":"https://pith.science/pith/SAAOD7KU5SY25T4BUNXK47CSJ3/bundle.json","state":"https://pith.science/pith/SAAOD7KU5SY25T4BUNXK47CSJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAAOD7KU5SY25T4BUNXK47CSJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SAAOD7KU5SY25T4BUNXK47CSJ3","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":"4abcbf860cbee3ab83f15b538518e95a76cf2c3a36e8ea30a08f05b2065dd66f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-15T05:24:22Z","title_canon_sha256":"3ad7581f7bf4d59b86d147390642b936c2f26e7fd014198c527d3a2fcc3391e5"},"schema_version":"1.0","source":{"id":"1902.05688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05688","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05688v1","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05688","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"SAAOD7KU5SY2","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"pith_short_16","alias_value":"SAAOD7KU5SY25T4B","created_at":"2026-06-04T20:13:54Z"},{"alias_kind":"pith_short_8","alias_value":"SAAOD7KU","created_at":"2026-06-04T20:13:54Z"}],"graph_snapshots":[{"event_id":"sha256:90b851a50a4485b76fa3ad630c03769fa3eee3b4298799e903298a8662e12db5","target":"graph","created_at":"2026-06-04T20:13:54Z","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/1902.05688/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Mea","authors_text":"Liwei Xu, Maojun Li, Yongping Cheng","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-15T05:24:22Z","title":"A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05688","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:c015554939fd3fa6cac0a33c64899bbe75199b1bebad1fc2e38039dc81b43a06","target":"record","created_at":"2026-06-04T20:13:54Z","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":"4abcbf860cbee3ab83f15b538518e95a76cf2c3a36e8ea30a08f05b2065dd66f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-15T05:24:22Z","title_canon_sha256":"3ad7581f7bf4d59b86d147390642b936c2f26e7fd014198c527d3a2fcc3391e5"},"schema_version":"1.0","source":{"id":"1902.05688","kind":"arxiv","version":1}},"canonical_sha256":"9000e1fd54ecb1aecf81a36eae7c524ee0164b291e8ddb5b45584875485271af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9000e1fd54ecb1aecf81a36eae7c524ee0164b291e8ddb5b45584875485271af","first_computed_at":"2026-06-04T20:13:54.139589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:54.139589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rRnGWtB2FA7NIxuKjHIwr1R88uocPdKAtVmg8jImu1Bfo8WYu0mNNvzK3yJavan6sR5d9uPIZpkMTuA3kWXQCA==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:54.140098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c015554939fd3fa6cac0a33c64899bbe75199b1bebad1fc2e38039dc81b43a06","sha256:90b851a50a4485b76fa3ad630c03769fa3eee3b4298799e903298a8662e12db5"],"state_sha256":"c4d367d2c1bc0fce3ea54f2c9b01d81297261329a5a69c43e3e68d35a7f86b42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KliGX8MtPo0vgN5+gHuK/osIL0Autr8Ie2XsNI/mlt6U/XjVjFzF4QUStbSrajRLAoCd9TppR+brv8kIdsAGCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:58:24.012459Z","bundle_sha256":"12b2f74f10a3d0cf55fde9798ada65b89f78301144610bb39eb02d4b5d6dc5df"}}