{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UADZXSLO3T36BAJBY6GVFXYVNK","short_pith_number":"pith:UADZXSLO","canonical_record":{"source":{"id":"2402.15150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-23T07:18:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b7c043a6353da07ef7547271c3ff0b5c32ba315e3cc80f3caa821e046a9ecc21","abstract_canon_sha256":"dedab2c59b13b87c4d0cf8b1d2534e70fa627fcb7ce6871a4958c5a763f5d498"},"schema_version":"1.0"},"canonical_sha256":"a0079bc96edcf7e08121c78d52df156a9d69d01f6e1e096597d9ba30372bfb3c","source":{"kind":"arxiv","id":"2402.15150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.15150","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"2402.15150v1","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.15150","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"UADZXSLO3T36","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"pith_short_16","alias_value":"UADZXSLO3T36BAJB","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"pith_short_8","alias_value":"UADZXSLO","created_at":"2026-07-05T07:48:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UADZXSLO3T36BAJBY6GVFXYVNK","target":"record","payload":{"canonical_record":{"source":{"id":"2402.15150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-23T07:18:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b7c043a6353da07ef7547271c3ff0b5c32ba315e3cc80f3caa821e046a9ecc21","abstract_canon_sha256":"dedab2c59b13b87c4d0cf8b1d2534e70fa627fcb7ce6871a4958c5a763f5d498"},"schema_version":"1.0"},"canonical_sha256":"a0079bc96edcf7e08121c78d52df156a9d69d01f6e1e096597d9ba30372bfb3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:48:36.484565Z","signature_b64":"IVpnwkVKhKRVrIhK8SrbKzlh+1XI1x0mQJNMYEaEAtYos0V0xjWq53x1mZtuTSWYlhwO8QcqE6kVrV6sAJlRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0079bc96edcf7e08121c78d52df156a9d69d01f6e1e096597d9ba30372bfb3c","last_reissued_at":"2026-07-05T07:48:36.484120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:48:36.484120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.15150","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":"2026-07-05T07:48:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HljmHO/BDb0RTsMOYtpTb4lDX5Owf5BVjIshDTtEYCXtoemAecxRlO/K4g9yPAjlUTqRd9R6viYfsAQ0C01nCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:47:44.451407Z"},"content_sha256":"e56d74616a4d2ac9669a81563997f1b88b6565f4864f6558a3607dc18fcb7ce2","schema_version":"1.0","event_id":"sha256:e56d74616a4d2ac9669a81563997f1b88b6565f4864f6558a3607dc18fcb7ce2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UADZXSLO3T36BAJBY6GVFXYVNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Runge--Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qifan Chen, Yulong Xing, Zheng Sun","submitted_at":"2024-02-23T07:18:22Z","abstract_excerpt":"In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the traditional method of lines framework and utilizes stage-dependent polynomial spaces for the spatial discretization operators. To be more specific, two different DG operators, associated with $\\mathcal{P}^k$ and $\\mathcal{P}^{k-1}$ piecewise polynomial spaces, are used at different RK stages. The resulting method is referred to as the sdRKDG method. It features fewer floating-point operations and may achieve larger time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.15150","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/2402.15150/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":"2026-07-05T07:48:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgffKiWnkYf8nXXTFyJETzejLnIbJLZXFt/f/hQvHZZl9fZhWL0GcEUIlqpqtedeSvhqhtjvpo6rA026dV20Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:47:44.451799Z"},"content_sha256":"1465c3ec3323c8580a91fe390d4d3d8ff543ce16e4b8e23bdf7d4b6c6387bf90","schema_version":"1.0","event_id":"sha256:1465c3ec3323c8580a91fe390d4d3d8ff543ce16e4b8e23bdf7d4b6c6387bf90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UADZXSLO3T36BAJBY6GVFXYVNK/bundle.json","state_url":"https://pith.science/pith/UADZXSLO3T36BAJBY6GVFXYVNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UADZXSLO3T36BAJBY6GVFXYVNK/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":"2026-07-06T15:47:44Z","links":{"resolver":"https://pith.science/pith/UADZXSLO3T36BAJBY6GVFXYVNK","bundle":"https://pith.science/pith/UADZXSLO3T36BAJBY6GVFXYVNK/bundle.json","state":"https://pith.science/pith/UADZXSLO3T36BAJBY6GVFXYVNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UADZXSLO3T36BAJBY6GVFXYVNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UADZXSLO3T36BAJBY6GVFXYVNK","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":"dedab2c59b13b87c4d0cf8b1d2534e70fa627fcb7ce6871a4958c5a763f5d498","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-23T07:18:22Z","title_canon_sha256":"b7c043a6353da07ef7547271c3ff0b5c32ba315e3cc80f3caa821e046a9ecc21"},"schema_version":"1.0","source":{"id":"2402.15150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.15150","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"2402.15150v1","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.15150","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"UADZXSLO3T36","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"pith_short_16","alias_value":"UADZXSLO3T36BAJB","created_at":"2026-07-05T07:48:36Z"},{"alias_kind":"pith_short_8","alias_value":"UADZXSLO","created_at":"2026-07-05T07:48:36Z"}],"graph_snapshots":[{"event_id":"sha256:1465c3ec3323c8580a91fe390d4d3d8ff543ce16e4b8e23bdf7d4b6c6387bf90","target":"graph","created_at":"2026-07-05T07:48:36Z","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/2402.15150/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the traditional method of lines framework and utilizes stage-dependent polynomial spaces for the spatial discretization operators. To be more specific, two different DG operators, associated with $\\mathcal{P}^k$ and $\\mathcal{P}^{k-1}$ piecewise polynomial spaces, are used at different RK stages. The resulting method is referred to as the sdRKDG method. It features fewer floating-point operations and may achieve larger time ","authors_text":"Qifan Chen, Yulong Xing, Zheng Sun","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-23T07:18:22Z","title":"The Runge--Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.15150","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:e56d74616a4d2ac9669a81563997f1b88b6565f4864f6558a3607dc18fcb7ce2","target":"record","created_at":"2026-07-05T07:48:36Z","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":"dedab2c59b13b87c4d0cf8b1d2534e70fa627fcb7ce6871a4958c5a763f5d498","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-23T07:18:22Z","title_canon_sha256":"b7c043a6353da07ef7547271c3ff0b5c32ba315e3cc80f3caa821e046a9ecc21"},"schema_version":"1.0","source":{"id":"2402.15150","kind":"arxiv","version":1}},"canonical_sha256":"a0079bc96edcf7e08121c78d52df156a9d69d01f6e1e096597d9ba30372bfb3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0079bc96edcf7e08121c78d52df156a9d69d01f6e1e096597d9ba30372bfb3c","first_computed_at":"2026-07-05T07:48:36.484120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:48:36.484120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IVpnwkVKhKRVrIhK8SrbKzlh+1XI1x0mQJNMYEaEAtYos0V0xjWq53x1mZtuTSWYlhwO8QcqE6kVrV6sAJlRCw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:48:36.484565Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.15150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e56d74616a4d2ac9669a81563997f1b88b6565f4864f6558a3607dc18fcb7ce2","sha256:1465c3ec3323c8580a91fe390d4d3d8ff543ce16e4b8e23bdf7d4b6c6387bf90"],"state_sha256":"33dc6f4432e9d168dbe2fe57df927da223afec480bbaec5f048735863f064b7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K9b5Zgm3h+xDhtq6BT+j3DHKv2jqSQ5SXzkN0XL34IHixiNAhkgZuUTbigj+EeoK4zqSyxksPzTGk3OXed6JCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:47:44.453716Z","bundle_sha256":"6fb290db3ee482f3df87f2535ded3e3b9a4fbf5dbe0b39229128d688c691b710"}}