{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZQILCPSPZU2PC7PAI7CTUGU5UF","short_pith_number":"pith:ZQILCPSP","canonical_record":{"source":{"id":"1809.09815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-26T05:31:12Z","cross_cats_sorted":[],"title_canon_sha256":"436829ecf6486140729f5f2b6446383fc2eb463012ea0aea87c22804192f9090","abstract_canon_sha256":"28d7c00d6420be0ec2a041706349f3c02b3cc5cf1851fbdc592dff6216eb2c54"},"schema_version":"1.0"},"canonical_sha256":"cc10b13e4fcd34f17de047c53a1a9da1787f09abec13bc27d1811fbc972bac3c","source":{"kind":"arxiv","id":"1809.09815","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09815","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09815v2","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09815","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZQILCPSPZU2P","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZQILCPSPZU2PC7PA","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZQILCPSP","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZQILCPSPZU2PC7PAI7CTUGU5UF","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-26T05:31:12Z","cross_cats_sorted":[],"title_canon_sha256":"436829ecf6486140729f5f2b6446383fc2eb463012ea0aea87c22804192f9090","abstract_canon_sha256":"28d7c00d6420be0ec2a041706349f3c02b3cc5cf1851fbdc592dff6216eb2c54"},"schema_version":"1.0"},"canonical_sha256":"cc10b13e4fcd34f17de047c53a1a9da1787f09abec13bc27d1811fbc972bac3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:30.204447Z","signature_b64":"emXcCXjkcduq+05Hdt8W4gmTok0Tgb4UK58A0DT194B++AIeCBd13XSPP8mf7IZGmY045OgtQgDFcbPbFHH4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc10b13e4fcd34f17de047c53a1a9da1787f09abec13bc27d1811fbc972bac3c","last_reissued_at":"2026-05-17T23:47:30.203804Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:30.203804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09815","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":"2026-05-17T23:47:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fc+3WumSMAyHEkQoKNAmRsp1uoBjleDn7HIg6liC3mUkmZGkktZflaIHpHXWSyu5KEjKZvXnXRhSfS8YkJ7nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:32:09.713527Z"},"content_sha256":"b3b627f3b919bc56aea6ca3877a25550e91935d54ee571ad2f84b0c3decc6ec0","schema_version":"1.0","event_id":"sha256:b3b627f3b919bc56aea6ca3877a25550e91935d54ee571ad2f84b0c3decc6ec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZQILCPSPZU2PC7PAI7CTUGU5UF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis and entropy stability of the line-based discontinuous Galerkin method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Per-Olof Persson, Will Pazner","submitted_at":"2018-09-26T05:31:12Z","abstract_excerpt":"We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09815","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":""},"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":"2026-05-17T23:47:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OsdXd1DvKfQ5bEE9M/j3k7X45cyzKTFy8cENHpWWQHURnLrOHq8WUGSU87xMmsCwM8asp7QmXTdEqFqk3XqBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:32:09.714165Z"},"content_sha256":"ea0d640ca5aa37332cf89b5644e9e7b0c93f2adba9d6930ab6490dcc5a2f8a7b","schema_version":"1.0","event_id":"sha256:ea0d640ca5aa37332cf89b5644e9e7b0c93f2adba9d6930ab6490dcc5a2f8a7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF/bundle.json","state_url":"https://pith.science/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF/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":"2026-05-30T23:32:09Z","links":{"resolver":"https://pith.science/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF","bundle":"https://pith.science/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF/bundle.json","state":"https://pith.science/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQILCPSPZU2PC7PAI7CTUGU5UF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZQILCPSPZU2PC7PAI7CTUGU5UF","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":"28d7c00d6420be0ec2a041706349f3c02b3cc5cf1851fbdc592dff6216eb2c54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-26T05:31:12Z","title_canon_sha256":"436829ecf6486140729f5f2b6446383fc2eb463012ea0aea87c22804192f9090"},"schema_version":"1.0","source":{"id":"1809.09815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09815","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09815v2","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09815","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZQILCPSPZU2P","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZQILCPSPZU2PC7PA","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZQILCPSP","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:ea0d640ca5aa37332cf89b5644e9e7b0c93f2adba9d6930ab6490dcc5a2f8a7b","target":"graph","created_at":"2026-05-17T23:47:30Z","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"},"paper":{"abstract_excerpt":"We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard","authors_text":"Per-Olof Persson, Will Pazner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-26T05:31:12Z","title":"Analysis and entropy stability of the line-based discontinuous Galerkin method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09815","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:b3b627f3b919bc56aea6ca3877a25550e91935d54ee571ad2f84b0c3decc6ec0","target":"record","created_at":"2026-05-17T23:47:30Z","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":"28d7c00d6420be0ec2a041706349f3c02b3cc5cf1851fbdc592dff6216eb2c54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-26T05:31:12Z","title_canon_sha256":"436829ecf6486140729f5f2b6446383fc2eb463012ea0aea87c22804192f9090"},"schema_version":"1.0","source":{"id":"1809.09815","kind":"arxiv","version":2}},"canonical_sha256":"cc10b13e4fcd34f17de047c53a1a9da1787f09abec13bc27d1811fbc972bac3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc10b13e4fcd34f17de047c53a1a9da1787f09abec13bc27d1811fbc972bac3c","first_computed_at":"2026-05-17T23:47:30.203804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:30.203804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"emXcCXjkcduq+05Hdt8W4gmTok0Tgb4UK58A0DT194B++AIeCBd13XSPP8mf7IZGmY045OgtQgDFcbPbFHH4CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:30.204447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3b627f3b919bc56aea6ca3877a25550e91935d54ee571ad2f84b0c3decc6ec0","sha256:ea0d640ca5aa37332cf89b5644e9e7b0c93f2adba9d6930ab6490dcc5a2f8a7b"],"state_sha256":"b097c48a11ea2ce4fd9db55b837d16a9e52f6fcc056e3369dd2583f5ffff82bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0xIGUNQzCESF+et+Hhgz0NILEQ1NHBVLbja6J001jyugcNskPLMr3KHomfq4LgdVYyNIUo4G0rKpTVlLHshJAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:32:09.717223Z","bundle_sha256":"2edd9d3cbc11a1a731d3408dd7ee19e1f1f2880bc9dc7628ba8bbf4ef1f2b2ef"}}