{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:QSUVFTNEV7HKR3UR24FPZYEYAS","short_pith_number":"pith:QSUVFTNE","canonical_record":{"source":{"id":"2007.09026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-17T14:41:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"223aaf3ea8350ce73851300f4636f7c48b308e307101539cc5f14d3dc1a0072b","abstract_canon_sha256":"7eff1c587c22b120964347bfbd61dc155514089892703d60df21ccd88084ba3a"},"schema_version":"1.0"},"canonical_sha256":"84a952cda4afcea8ee91d70afce09804ab573562d3ac693cf378aecca8e0aa4b","source":{"kind":"arxiv","id":"2007.09026","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.09026","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"2007.09026v2","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.09026","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"QSUVFTNEV7HK","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"pith_short_16","alias_value":"QSUVFTNEV7HKR3UR","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"pith_short_8","alias_value":"QSUVFTNE","created_at":"2026-07-05T03:29:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:QSUVFTNEV7HKR3UR24FPZYEYAS","target":"record","payload":{"canonical_record":{"source":{"id":"2007.09026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-17T14:41:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"223aaf3ea8350ce73851300f4636f7c48b308e307101539cc5f14d3dc1a0072b","abstract_canon_sha256":"7eff1c587c22b120964347bfbd61dc155514089892703d60df21ccd88084ba3a"},"schema_version":"1.0"},"canonical_sha256":"84a952cda4afcea8ee91d70afce09804ab573562d3ac693cf378aecca8e0aa4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:29:13.994913Z","signature_b64":"IJ2wlxBMmR7R80g7een1YMEUGi8vf2JdROOj1Q5UfLKG9d0zlEswAJgyz8Nu0STmOD3F40l9Au2GLOOKFFPjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84a952cda4afcea8ee91d70afce09804ab573562d3ac693cf378aecca8e0aa4b","last_reissued_at":"2026-07-05T03:29:13.994447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:29:13.994447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.09026","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":"2026-07-05T03:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XJ6QYuG6XPjKko+JOe29fQLmVFDJa5I542finH2r4aofH5NSLCJECXZ42oVuW8qjdUUJdLUdXKca3ThDIPIlCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:18:21.414115Z"},"content_sha256":"5604bb3621f06ce8bc16dc13503e05f3fa4edb06bc3f8bc8fc217f4ddfeaba23","schema_version":"1.0","event_id":"sha256:5604bb3621f06ce8bc16dc13503e05f3fa4edb06bc3f8bc8fc217f4ddfeaba23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:QSUVFTNEV7HKR3UR24FPZYEYAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability issues of entropy-stable and/or split-form high-order schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Florian J. Hindenlang, Gregor J. Gassner, Magnus Sv\\\"ard","submitted_at":"2020-07-17T14:41:41Z","abstract_excerpt":"The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conserving fluxes, approximating non-linear conservation laws. Our main finding is that local energy stability, i.e., the numerical growth rate does not exceed the growth rate of the continuous problem, is not guaranteed even when the scheme is non-linearly stable and that this may have adverse implications for simulation results. We show that entropy-conserving two-point fluxes are inherently locally energy unstable, as the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.09026","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/2007.09026/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":"2026-07-05T03:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mr0u0FSyOMTIBRIS2VB1la+u0IIVGEXpMbBP8UiHfLZPML3fY07Sc15+6+/2CWm80DrS5N6yLDHCT3WwG/ecCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:18:21.414986Z"},"content_sha256":"da6be0dfb1db564280e6ebe405fa2d72d17297761bf8f1d2187d076bfe851d11","schema_version":"1.0","event_id":"sha256:da6be0dfb1db564280e6ebe405fa2d72d17297761bf8f1d2187d076bfe851d11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSUVFTNEV7HKR3UR24FPZYEYAS/bundle.json","state_url":"https://pith.science/pith/QSUVFTNEV7HKR3UR24FPZYEYAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSUVFTNEV7HKR3UR24FPZYEYAS/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":"2026-08-06T08:18:21Z","links":{"resolver":"https://pith.science/pith/QSUVFTNEV7HKR3UR24FPZYEYAS","bundle":"https://pith.science/pith/QSUVFTNEV7HKR3UR24FPZYEYAS/bundle.json","state":"https://pith.science/pith/QSUVFTNEV7HKR3UR24FPZYEYAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSUVFTNEV7HKR3UR24FPZYEYAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QSUVFTNEV7HKR3UR24FPZYEYAS","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":"7eff1c587c22b120964347bfbd61dc155514089892703d60df21ccd88084ba3a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-17T14:41:41Z","title_canon_sha256":"223aaf3ea8350ce73851300f4636f7c48b308e307101539cc5f14d3dc1a0072b"},"schema_version":"1.0","source":{"id":"2007.09026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.09026","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"2007.09026v2","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.09026","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"QSUVFTNEV7HK","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"pith_short_16","alias_value":"QSUVFTNEV7HKR3UR","created_at":"2026-07-05T03:29:13Z"},{"alias_kind":"pith_short_8","alias_value":"QSUVFTNE","created_at":"2026-07-05T03:29:13Z"}],"graph_snapshots":[{"event_id":"sha256:da6be0dfb1db564280e6ebe405fa2d72d17297761bf8f1d2187d076bfe851d11","target":"graph","created_at":"2026-07-05T03:29:13Z","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/2007.09026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conserving fluxes, approximating non-linear conservation laws. Our main finding is that local energy stability, i.e., the numerical growth rate does not exceed the growth rate of the continuous problem, is not guaranteed even when the scheme is non-linearly stable and that this may have adverse implications for simulation results. We show that entropy-conserving two-point fluxes are inherently locally energy unstable, as the","authors_text":"Florian J. Hindenlang, Gregor J. Gassner, Magnus Sv\\\"ard","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-17T14:41:41Z","title":"Stability issues of entropy-stable and/or split-form high-order schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.09026","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":"sha256:5604bb3621f06ce8bc16dc13503e05f3fa4edb06bc3f8bc8fc217f4ddfeaba23","target":"record","created_at":"2026-07-05T03:29:13Z","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":"7eff1c587c22b120964347bfbd61dc155514089892703d60df21ccd88084ba3a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-17T14:41:41Z","title_canon_sha256":"223aaf3ea8350ce73851300f4636f7c48b308e307101539cc5f14d3dc1a0072b"},"schema_version":"1.0","source":{"id":"2007.09026","kind":"arxiv","version":2}},"canonical_sha256":"84a952cda4afcea8ee91d70afce09804ab573562d3ac693cf378aecca8e0aa4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84a952cda4afcea8ee91d70afce09804ab573562d3ac693cf378aecca8e0aa4b","first_computed_at":"2026-07-05T03:29:13.994447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:29:13.994447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJ2wlxBMmR7R80g7een1YMEUGi8vf2JdROOj1Q5UfLKG9d0zlEswAJgyz8Nu0STmOD3F40l9Au2GLOOKFFPjAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:29:13.994913Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.09026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5604bb3621f06ce8bc16dc13503e05f3fa4edb06bc3f8bc8fc217f4ddfeaba23","sha256:da6be0dfb1db564280e6ebe405fa2d72d17297761bf8f1d2187d076bfe851d11"],"state_sha256":"1e0676be1c81483d55f65216243a1ddc3533a35fec15fe2166afbae97d7f6a57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ePsQaaa8RmFRwRxiX+Qvn/8tIs45OzZp/Qg54XDAXw4RsX+7xuDjXh61tA3KQA7HllQcDBWxnmJGDy1RpR3WAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T08:18:21.425957Z","bundle_sha256":"a6e15d96fc1ecc1e9ab7dd46b76e88bfad8d36a003fbe072906a7637eaadc01a"}}