{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:4YK4VFUQPQR75XELUGTN2KMUN4","short_pith_number":"pith:4YK4VFUQ","canonical_record":{"source":{"id":"2107.13910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-29T11:40:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"302ae79d8e0b4eba37802dc01beb351077b7d586a7c651d5d586e3de1a61a22e","abstract_canon_sha256":"95fbaa3d6f52b4a8e14e5eb57d66a6e15eaecba514574112fa4e3e560e21c217"},"schema_version":"1.0"},"canonical_sha256":"e615ca96907c23fedc8ba1a6dd29946f0596a5fa9fd73f32393d6cb24078b8a6","source":{"kind":"arxiv","id":"2107.13910","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.13910","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2107.13910v2","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13910","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"4YK4VFUQPQR7","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"4YK4VFUQPQR75XEL","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"4YK4VFUQ","created_at":"2026-07-05T04:03:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:4YK4VFUQPQR75XELUGTN2KMUN4","target":"record","payload":{"canonical_record":{"source":{"id":"2107.13910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-29T11:40:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"302ae79d8e0b4eba37802dc01beb351077b7d586a7c651d5d586e3de1a61a22e","abstract_canon_sha256":"95fbaa3d6f52b4a8e14e5eb57d66a6e15eaecba514574112fa4e3e560e21c217"},"schema_version":"1.0"},"canonical_sha256":"e615ca96907c23fedc8ba1a6dd29946f0596a5fa9fd73f32393d6cb24078b8a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:03:49.531148Z","signature_b64":"VQzbFLsdTP0Npf0DNQrC+YTfvEwW82jAR+wiD0trUNWLKhhWaNVr6eL2YsypGzpz/d92TxWX0AnB6deDG92mAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e615ca96907c23fedc8ba1a6dd29946f0596a5fa9fd73f32393d6cb24078b8a6","last_reissued_at":"2026-07-05T04:03:49.530662Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:03:49.530662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.13910","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":"2026-07-05T04:03:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8qmUPVzW3LWpOsaQuFK1GMCcbydC8HHCw5MayEilMm/6sZ+IClbPVDgUI0/cXR2i+snwqORsuPR34qEONqjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:26:17.400077Z"},"content_sha256":"b3959b7e355870fa92c3dee79001fad272c5ae8104d70c8ce910baba44f65ecc","schema_version":"1.0","event_id":"sha256:b3959b7e355870fa92c3dee79001fad272c5ae8104d70c8ce910baba44f65ecc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:4YK4VFUQPQR75XELUGTN2KMUN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High order finite difference WENO methods with unequal-sized sub-stencils for the Degasperis-Procesi type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Huiwen Xue, Jianfang Lin, Xinghui Zhong, Yan Yu","submitted_at":"2021-07-29T11:40:37Z","abstract_excerpt":"In this paper, we develop two finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and $\\mu$-Degasperis-Procesi ($\\mu$DP) equations, which contain nonlinear high order derivatives, and possibly peakon solutions or shock waves. By introducing auxiliary variable(s), we rewrite the DP equation as a hyperbolic-elliptic system, and the \\mdp equation as a first order system. Then we choose a linear finite difference scheme with suitable order of accuracy for the auxiliary variable(s), and two finite difference W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13910","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/2107.13910/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":"2026-07-05T04:03:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SaHuOeyPmDJohtECQTVmrvoBlSUk93N2hVoLgfvzbLyyjS8h7u2XQEgLmYFx3c+20jNN3/V5/8p00i5oI1+wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:26:17.400609Z"},"content_sha256":"acb9e3f8e3a9dfad6b6d0e9a24251402212d7031f7ac93014243ebf91b05ea90","schema_version":"1.0","event_id":"sha256:acb9e3f8e3a9dfad6b6d0e9a24251402212d7031f7ac93014243ebf91b05ea90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YK4VFUQPQR75XELUGTN2KMUN4/bundle.json","state_url":"https://pith.science/pith/4YK4VFUQPQR75XELUGTN2KMUN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YK4VFUQPQR75XELUGTN2KMUN4/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":"2026-08-15T23:26:17Z","links":{"resolver":"https://pith.science/pith/4YK4VFUQPQR75XELUGTN2KMUN4","bundle":"https://pith.science/pith/4YK4VFUQPQR75XELUGTN2KMUN4/bundle.json","state":"https://pith.science/pith/4YK4VFUQPQR75XELUGTN2KMUN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YK4VFUQPQR75XELUGTN2KMUN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4YK4VFUQPQR75XELUGTN2KMUN4","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":"95fbaa3d6f52b4a8e14e5eb57d66a6e15eaecba514574112fa4e3e560e21c217","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-29T11:40:37Z","title_canon_sha256":"302ae79d8e0b4eba37802dc01beb351077b7d586a7c651d5d586e3de1a61a22e"},"schema_version":"1.0","source":{"id":"2107.13910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.13910","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2107.13910v2","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13910","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"4YK4VFUQPQR7","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"4YK4VFUQPQR75XEL","created_at":"2026-07-05T04:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"4YK4VFUQ","created_at":"2026-07-05T04:03:49Z"}],"graph_snapshots":[{"event_id":"sha256:acb9e3f8e3a9dfad6b6d0e9a24251402212d7031f7ac93014243ebf91b05ea90","target":"graph","created_at":"2026-07-05T04:03:49Z","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/2107.13910/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we develop two finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and $\\mu$-Degasperis-Procesi ($\\mu$DP) equations, which contain nonlinear high order derivatives, and possibly peakon solutions or shock waves. By introducing auxiliary variable(s), we rewrite the DP equation as a hyperbolic-elliptic system, and the \\mdp equation as a first order system. Then we choose a linear finite difference scheme with suitable order of accuracy for the auxiliary variable(s), and two finite difference W","authors_text":"Huiwen Xue, Jianfang Lin, Xinghui Zhong, Yan Yu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-29T11:40:37Z","title":"High order finite difference WENO methods with unequal-sized sub-stencils for the Degasperis-Procesi type equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13910","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:b3959b7e355870fa92c3dee79001fad272c5ae8104d70c8ce910baba44f65ecc","target":"record","created_at":"2026-07-05T04:03:49Z","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":"95fbaa3d6f52b4a8e14e5eb57d66a6e15eaecba514574112fa4e3e560e21c217","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-07-29T11:40:37Z","title_canon_sha256":"302ae79d8e0b4eba37802dc01beb351077b7d586a7c651d5d586e3de1a61a22e"},"schema_version":"1.0","source":{"id":"2107.13910","kind":"arxiv","version":2}},"canonical_sha256":"e615ca96907c23fedc8ba1a6dd29946f0596a5fa9fd73f32393d6cb24078b8a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e615ca96907c23fedc8ba1a6dd29946f0596a5fa9fd73f32393d6cb24078b8a6","first_computed_at":"2026-07-05T04:03:49.530662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:03:49.530662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VQzbFLsdTP0Npf0DNQrC+YTfvEwW82jAR+wiD0trUNWLKhhWaNVr6eL2YsypGzpz/d92TxWX0AnB6deDG92mAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:03:49.531148Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.13910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3959b7e355870fa92c3dee79001fad272c5ae8104d70c8ce910baba44f65ecc","sha256:acb9e3f8e3a9dfad6b6d0e9a24251402212d7031f7ac93014243ebf91b05ea90"],"state_sha256":"694053c8eb866f3cb47a5ab321951b58fc5ab7db4432bc6f01a6fca74391b3ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+bIa9hEyfxk7RmXN1ajGb5EzAG6JIdVXNRrE70qdaEhE1TpfFsPTaaUUnxDKLpdXUrvkuYFdn+MPiZBbi+Z4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T23:26:17.406073Z","bundle_sha256":"288e9713567c2eb42faad07ec61bfef23c02fc959d5e725ee7d20659e20ae799"}}