{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VSYM5IBKW2UVVULM2666VXPWBQ","short_pith_number":"pith:VSYM5IBK","canonical_record":{"source":{"id":"1908.09917","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T04:36:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ee5b46dea5395ce49ac72929505b32ce447cb8c911be9dc74511b69917f0d746","abstract_canon_sha256":"057bb985775275b3db0cb2c8544e2532ddd17927c349a755e15ee7b3e2a57315"},"schema_version":"1.0"},"canonical_sha256":"acb0cea02ab6a95ad16cd7bdeaddf60c16d280f0c82bdb8aa98945c4a50c1e31","source":{"kind":"arxiv","id":"1908.09917","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09917","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09917v4","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09917","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"VSYM5IBKW2UV","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"pith_short_16","alias_value":"VSYM5IBKW2UVVULM","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"pith_short_8","alias_value":"VSYM5IBK","created_at":"2026-07-05T01:54:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VSYM5IBKW2UVVULM2666VXPWBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.09917","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T04:36:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ee5b46dea5395ce49ac72929505b32ce447cb8c911be9dc74511b69917f0d746","abstract_canon_sha256":"057bb985775275b3db0cb2c8544e2532ddd17927c349a755e15ee7b3e2a57315"},"schema_version":"1.0"},"canonical_sha256":"acb0cea02ab6a95ad16cd7bdeaddf60c16d280f0c82bdb8aa98945c4a50c1e31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:54:41.249252Z","signature_b64":"K+CAmBeriRxSoTL6VjDZGygTYwBBE4ya5wu5+qpYCRmxLWbMkuB5jcCH2oe4ZMCDU9XH2Pp3HuEyXEeE+aViCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acb0cea02ab6a95ad16cd7bdeaddf60c16d280f0c82bdb8aa98945c4a50c1e31","last_reissued_at":"2026-07-05T01:54:41.248818Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:54:41.248818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.09917","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMzl6cRrtsQflcixgqNZvOtSsVum03iUsW5v6x4BluvZ8Kdl5VB6m37J9u7NFa12ZSD5wvfJDYlBDoDNMDy+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:17:15.395523Z"},"content_sha256":"35ab289027ccf133d22359a21fef41b946be4dca5ee0470162b7fd91dad133cb","schema_version":"1.0","event_id":"sha256:35ab289027ccf133d22359a21fef41b946be4dca5ee0470162b7fd91dad133cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VSYM5IBKW2UVVULM2666VXPWBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical study on the effect of geometric approximation error in the numerical solution of PDEs using a high-order curvilinear mesh","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Joaquim Peiro, Julian Marcon, Sehun Chun, Spencer J. Sherwin","submitted_at":"2019-08-23T04:36:21Z","abstract_excerpt":"When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09917","kind":"arxiv","version":4},"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/1908.09917/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":"2026-07-05T01:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nB+mwZBsZgNZ3jLO6n+wlZka7ItCypqViq0gwmffu90iuaSnQ40TcfQ8pefuZkifCKWU8HZOBR8rXLCpcKMdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:17:15.396155Z"},"content_sha256":"ac61f8b14f802ea45a3d9cd3a9a23a7889da1bb8cd7a8daae3a0ec045cbf9652","schema_version":"1.0","event_id":"sha256:ac61f8b14f802ea45a3d9cd3a9a23a7889da1bb8cd7a8daae3a0ec045cbf9652"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSYM5IBKW2UVVULM2666VXPWBQ/bundle.json","state_url":"https://pith.science/pith/VSYM5IBKW2UVVULM2666VXPWBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSYM5IBKW2UVVULM2666VXPWBQ/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":"2026-08-16T10:17:15Z","links":{"resolver":"https://pith.science/pith/VSYM5IBKW2UVVULM2666VXPWBQ","bundle":"https://pith.science/pith/VSYM5IBKW2UVVULM2666VXPWBQ/bundle.json","state":"https://pith.science/pith/VSYM5IBKW2UVVULM2666VXPWBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSYM5IBKW2UVVULM2666VXPWBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VSYM5IBKW2UVVULM2666VXPWBQ","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":"057bb985775275b3db0cb2c8544e2532ddd17927c349a755e15ee7b3e2a57315","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T04:36:21Z","title_canon_sha256":"ee5b46dea5395ce49ac72929505b32ce447cb8c911be9dc74511b69917f0d746"},"schema_version":"1.0","source":{"id":"1908.09917","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09917","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09917v4","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09917","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"VSYM5IBKW2UV","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"pith_short_16","alias_value":"VSYM5IBKW2UVVULM","created_at":"2026-07-05T01:54:41Z"},{"alias_kind":"pith_short_8","alias_value":"VSYM5IBK","created_at":"2026-07-05T01:54:41Z"}],"graph_snapshots":[{"event_id":"sha256:ac61f8b14f802ea45a3d9cd3a9a23a7889da1bb8cd7a8daae3a0ec045cbf9652","target":"graph","created_at":"2026-07-05T01:54:41Z","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/1908.09917/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. Th","authors_text":"Joaquim Peiro, Julian Marcon, Sehun Chun, Spencer J. Sherwin","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T04:36:21Z","title":"Numerical study on the effect of geometric approximation error in the numerical solution of PDEs using a high-order curvilinear mesh"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09917","kind":"arxiv","version":4},"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":"sha256:35ab289027ccf133d22359a21fef41b946be4dca5ee0470162b7fd91dad133cb","target":"record","created_at":"2026-07-05T01:54:41Z","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":"057bb985775275b3db0cb2c8544e2532ddd17927c349a755e15ee7b3e2a57315","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-23T04:36:21Z","title_canon_sha256":"ee5b46dea5395ce49ac72929505b32ce447cb8c911be9dc74511b69917f0d746"},"schema_version":"1.0","source":{"id":"1908.09917","kind":"arxiv","version":4}},"canonical_sha256":"acb0cea02ab6a95ad16cd7bdeaddf60c16d280f0c82bdb8aa98945c4a50c1e31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acb0cea02ab6a95ad16cd7bdeaddf60c16d280f0c82bdb8aa98945c4a50c1e31","first_computed_at":"2026-07-05T01:54:41.248818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:54:41.248818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K+CAmBeriRxSoTL6VjDZGygTYwBBE4ya5wu5+qpYCRmxLWbMkuB5jcCH2oe4ZMCDU9XH2Pp3HuEyXEeE+aViCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:54:41.249252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09917","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35ab289027ccf133d22359a21fef41b946be4dca5ee0470162b7fd91dad133cb","sha256:ac61f8b14f802ea45a3d9cd3a9a23a7889da1bb8cd7a8daae3a0ec045cbf9652"],"state_sha256":"f56efde303c15327a9f6825d479ac8caaee92ed3dd2717b1c25f9feb423ac1db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kuq7bynKHqCS09jDOVJxv7bhwzpvy+NmSgPA5FCmbTqUVKfNCgfoAHbKyrPE2HRPw3NPDnMjOoWkAEktJbQRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:17:15.410700Z","bundle_sha256":"2781486c89bf9a24ed5e655c1a77b9ccaeb22398bd4e8593688948c5945c9832"}}