{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OCUXIO5O3FF2DPOD4OLLEYJF7H","short_pith_number":"pith:OCUXIO5O","canonical_record":{"source":{"id":"2608.06642","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-08-06T23:20:39Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9e736b053cf6988c4ceccdd9fcfe8d02d10594a5c17f9553dd84945f91762dbd","abstract_canon_sha256":"3808f7d2003b6d8b3e081c16846f0b4250199258ca0d7d722fbc6825dc60943b"},"schema_version":"1.0"},"canonical_sha256":"70a9743baed94ba1bdc3e396b26125f9c45a1b30825d2c1f00c1b56b1029c520","source":{"kind":"arxiv","id":"2608.06642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06642","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06642v1","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06642","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"OCUXIO5O3FF2","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_16","alias_value":"OCUXIO5O3FF2DPOD","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_8","alias_value":"OCUXIO5O","created_at":"2026-08-10T01:11:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OCUXIO5O3FF2DPOD4OLLEYJF7H","target":"record","payload":{"canonical_record":{"source":{"id":"2608.06642","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-08-06T23:20:39Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9e736b053cf6988c4ceccdd9fcfe8d02d10594a5c17f9553dd84945f91762dbd","abstract_canon_sha256":"3808f7d2003b6d8b3e081c16846f0b4250199258ca0d7d722fbc6825dc60943b"},"schema_version":"1.0"},"canonical_sha256":"70a9743baed94ba1bdc3e396b26125f9c45a1b30825d2c1f00c1b56b1029c520","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-10T01:11:34.219718Z","signature_b64":"BsQFRaMGVkMCUhkFkAciHlYThVn5gAkKSsH6AsULLm0PcH3oU8TNA33PEb+hd2PXTR//VjBoyL4RK1JH5vH2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70a9743baed94ba1bdc3e396b26125f9c45a1b30825d2c1f00c1b56b1029c520","last_reissued_at":"2026-08-10T01:11:34.217387Z","signature_status":"signed_v1","first_computed_at":"2026-08-10T01:11:34.217387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.06642","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":"2026-08-10T01:11:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3fCpNq/kKvie00H5hRt4eJcjJicIlxtqElOKQTwBoe74jyqc61ggTf5O42oTi6E9AcHCKSBtYlzNWKf62nH3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:38:43.495053Z"},"content_sha256":"a5d75c5f67b27eda11e43a632e344070223aac51c4bb9a1740a1fcde0478c64c","schema_version":"1.0","event_id":"sha256:a5d75c5f67b27eda11e43a632e344070223aac51c4bb9a1740a1fcde0478c64c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OCUXIO5O3FF2DPOD4OLLEYJF7H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The error estimate of entropy-stable discontinuous Galerkin methods for hyperbolic conservation laws","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chi-Wang Shu, Xu-Kun Chen, Yong Liu","submitted_at":"2026-08-06T23:20:39Z","abstract_excerpt":"Entropy inequalities are fundamental to the well-posedness of hyperbolic conservation laws, providing the essential criterion for selecting the physically admissible solution among infinitely many weak solutions. Chen and Shu [J. Comput. Phys. 345 (2017)] proposed a unified framework for constructing high-order discontinuous Galerkin (DG) methods that satisfy entropy inequalities for any given entropy via specific numerical quadrature; however, their accompanying error analysis was limited to the truncation error level, leaving a critical gap in the rigorous convergence theory for these entrop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06642","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/2608.06642/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":"2026-08-10T01:11:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZVPEi2pUkiLhARePazKpCjVN/cK/G6qZdInc1OJYGIk+D/klh0JJuVvQsG8EK795QdZCkNYTx0XrWlqpMDuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:38:43.495581Z"},"content_sha256":"11f3dede6666ccf360146891299c6459aaa3598a176a052310ad89aa7c935ab6","schema_version":"1.0","event_id":"sha256:11f3dede6666ccf360146891299c6459aaa3598a176a052310ad89aa7c935ab6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H/bundle.json","state_url":"https://pith.science/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H/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":"2026-08-10T23:38:43Z","links":{"resolver":"https://pith.science/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H","bundle":"https://pith.science/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H/bundle.json","state":"https://pith.science/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OCUXIO5O3FF2DPOD4OLLEYJF7H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OCUXIO5O3FF2DPOD4OLLEYJF7H","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":"3808f7d2003b6d8b3e081c16846f0b4250199258ca0d7d722fbc6825dc60943b","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-08-06T23:20:39Z","title_canon_sha256":"9e736b053cf6988c4ceccdd9fcfe8d02d10594a5c17f9553dd84945f91762dbd"},"schema_version":"1.0","source":{"id":"2608.06642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06642","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06642v1","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06642","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"OCUXIO5O3FF2","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_16","alias_value":"OCUXIO5O3FF2DPOD","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_8","alias_value":"OCUXIO5O","created_at":"2026-08-10T01:11:34Z"}],"graph_snapshots":[{"event_id":"sha256:11f3dede6666ccf360146891299c6459aaa3598a176a052310ad89aa7c935ab6","target":"graph","created_at":"2026-08-10T01:11:34Z","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/2608.06642/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Entropy inequalities are fundamental to the well-posedness of hyperbolic conservation laws, providing the essential criterion for selecting the physically admissible solution among infinitely many weak solutions. Chen and Shu [J. Comput. Phys. 345 (2017)] proposed a unified framework for constructing high-order discontinuous Galerkin (DG) methods that satisfy entropy inequalities for any given entropy via specific numerical quadrature; however, their accompanying error analysis was limited to the truncation error level, leaving a critical gap in the rigorous convergence theory for these entrop","authors_text":"Chi-Wang Shu, Xu-Kun Chen, Yong Liu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-08-06T23:20:39Z","title":"The error estimate of entropy-stable discontinuous Galerkin methods for hyperbolic conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06642","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:a5d75c5f67b27eda11e43a632e344070223aac51c4bb9a1740a1fcde0478c64c","target":"record","created_at":"2026-08-10T01:11:34Z","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":"3808f7d2003b6d8b3e081c16846f0b4250199258ca0d7d722fbc6825dc60943b","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-08-06T23:20:39Z","title_canon_sha256":"9e736b053cf6988c4ceccdd9fcfe8d02d10594a5c17f9553dd84945f91762dbd"},"schema_version":"1.0","source":{"id":"2608.06642","kind":"arxiv","version":1}},"canonical_sha256":"70a9743baed94ba1bdc3e396b26125f9c45a1b30825d2c1f00c1b56b1029c520","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70a9743baed94ba1bdc3e396b26125f9c45a1b30825d2c1f00c1b56b1029c520","first_computed_at":"2026-08-10T01:11:34.217387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-10T01:11:34.217387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BsQFRaMGVkMCUhkFkAciHlYThVn5gAkKSsH6AsULLm0PcH3oU8TNA33PEb+hd2PXTR//VjBoyL4RK1JH5vH2Dw==","signature_status":"signed_v1","signed_at":"2026-08-10T01:11:34.219718Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5d75c5f67b27eda11e43a632e344070223aac51c4bb9a1740a1fcde0478c64c","sha256:11f3dede6666ccf360146891299c6459aaa3598a176a052310ad89aa7c935ab6"],"state_sha256":"11c1c88a5af841a1afc99f60bbf8f68450ec598db28869b25428d79b10fdfb43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L+BKRMEDpuYb+LH5x1CsFEuzCRUDZbCFuSawvSeZ8Pj3mXqddCxdGhSbf1B/sllPEFdSBv4XMhWWi86dao7yCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T23:38:43.501375Z","bundle_sha256":"b14b3fe796256979b0d9d4245e04bada7b1736dafbacb20e21d2845b8bd93206"}}