{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:Q7DLKRBYUGR6I7QKTYHH5PMVMA","short_pith_number":"pith:Q7DLKRBY","canonical_record":{"source":{"id":"2411.14977","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-22T14:36:42Z","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"title_canon_sha256":"5b2e8307cd7dbd7abd61c4443863b96b651d7470266c27cce2b0fee88eaa6178","abstract_canon_sha256":"a7b0453b58e20f1b9f5ff11c84827f0d76ff1327779204d2f6f53b31535375e3"},"schema_version":"1.0"},"canonical_sha256":"87c6b54438a1a3e47e0a9e0e7ebd95601278b66248d66784c75a280b4af4c715","source":{"kind":"arxiv","id":"2411.14977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14977","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14977v1","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14977","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"Q7DLKRBYUGR6","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"pith_short_16","alias_value":"Q7DLKRBYUGR6I7QK","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"pith_short_8","alias_value":"Q7DLKRBY","created_at":"2026-07-05T09:39:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:Q7DLKRBYUGR6I7QKTYHH5PMVMA","target":"record","payload":{"canonical_record":{"source":{"id":"2411.14977","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-22T14:36:42Z","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"title_canon_sha256":"5b2e8307cd7dbd7abd61c4443863b96b651d7470266c27cce2b0fee88eaa6178","abstract_canon_sha256":"a7b0453b58e20f1b9f5ff11c84827f0d76ff1327779204d2f6f53b31535375e3"},"schema_version":"1.0"},"canonical_sha256":"87c6b54438a1a3e47e0a9e0e7ebd95601278b66248d66784c75a280b4af4c715","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:14.470343Z","signature_b64":"vL1aTdkBDfL5jJxf+xK2YUL0kr/4uEVaO4I8TJfms9r91i9wFunWTujL6bAh2blw5ek91TZ45N/T7ckpITHYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87c6b54438a1a3e47e0a9e0e7ebd95601278b66248d66784c75a280b4af4c715","last_reissued_at":"2026-07-05T09:39:14.469932Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:14.469932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.14977","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":"2026-07-05T09:39:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vcd9pzmYXaOUDx/uW7vCibO/McGeWxU/IQ3EDpQ2nBFHYqppMxTZSNHy26hcax7w61o6UgZ589FC2ulxW/8rCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:29:38.082288Z"},"content_sha256":"8f193f3c726a31b0b9db8b26064e615643d2151697152657761c2807a9210dfb","schema_version":"1.0","event_id":"sha256:8f193f3c726a31b0b9db8b26064e615643d2151697152657761c2807a9210dfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:Q7DLKRBYUGR6I7QKTYHH5PMVMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A p-Multigrid Accelerated Nodal Spectral Element Method for Free-Surface Incompressible Navier-Stokes Model of Nonlinear Water Waves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Allan P. Engsig-Karup, Anders Melander, Spencer J. Sherwin, Wojciech Laskowski","submitted_at":"2024-11-22T14:36:42Z","abstract_excerpt":"We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element method is inspired by the related work by Engsig-Karup et al. (2016) and is based on nodal Lagrange basis functions, mass matrix-based integration and gradient recovery using global $L^2$ projections. The resulting model leverages the high-order accurate -- possibly exponential -- error convergence and has support for geometric flexibility allowing for computa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14977","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/2411.14977/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":"2026-07-05T09:39:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KsK0Bk0+ExadK1piisX5wsAN63tzdTDw5iCvI6+YBCwrjKE8mO5qxsqyvb688PwsKRFXt1k2osLr3w1xhA7jCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:29:38.086104Z"},"content_sha256":"d382ddee85ae3e46b290eeae59dbf9bf935814bb32ef35cb7a74233471463416","schema_version":"1.0","event_id":"sha256:d382ddee85ae3e46b290eeae59dbf9bf935814bb32ef35cb7a74233471463416"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA/bundle.json","state_url":"https://pith.science/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA/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":"2026-08-13T00:29:38Z","links":{"resolver":"https://pith.science/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA","bundle":"https://pith.science/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA/bundle.json","state":"https://pith.science/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7DLKRBYUGR6I7QKTYHH5PMVMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:Q7DLKRBYUGR6I7QKTYHH5PMVMA","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":"a7b0453b58e20f1b9f5ff11c84827f0d76ff1327779204d2f6f53b31535375e3","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-22T14:36:42Z","title_canon_sha256":"5b2e8307cd7dbd7abd61c4443863b96b651d7470266c27cce2b0fee88eaa6178"},"schema_version":"1.0","source":{"id":"2411.14977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14977","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14977v1","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14977","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"Q7DLKRBYUGR6","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"pith_short_16","alias_value":"Q7DLKRBYUGR6I7QK","created_at":"2026-07-05T09:39:14Z"},{"alias_kind":"pith_short_8","alias_value":"Q7DLKRBY","created_at":"2026-07-05T09:39:14Z"}],"graph_snapshots":[{"event_id":"sha256:d382ddee85ae3e46b290eeae59dbf9bf935814bb32ef35cb7a74233471463416","target":"graph","created_at":"2026-07-05T09:39:14Z","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/2411.14977/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element method is inspired by the related work by Engsig-Karup et al. (2016) and is based on nodal Lagrange basis functions, mass matrix-based integration and gradient recovery using global $L^2$ projections. The resulting model leverages the high-order accurate -- possibly exponential -- error convergence and has support for geometric flexibility allowing for computa","authors_text":"Allan P. Engsig-Karup, Anders Melander, Spencer J. Sherwin, Wojciech Laskowski","cross_cats":["cs.NA","physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-22T14:36:42Z","title":"A p-Multigrid Accelerated Nodal Spectral Element Method for Free-Surface Incompressible Navier-Stokes Model of Nonlinear Water Waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14977","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":"sha256:8f193f3c726a31b0b9db8b26064e615643d2151697152657761c2807a9210dfb","target":"record","created_at":"2026-07-05T09:39:14Z","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":"a7b0453b58e20f1b9f5ff11c84827f0d76ff1327779204d2f6f53b31535375e3","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-11-22T14:36:42Z","title_canon_sha256":"5b2e8307cd7dbd7abd61c4443863b96b651d7470266c27cce2b0fee88eaa6178"},"schema_version":"1.0","source":{"id":"2411.14977","kind":"arxiv","version":1}},"canonical_sha256":"87c6b54438a1a3e47e0a9e0e7ebd95601278b66248d66784c75a280b4af4c715","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87c6b54438a1a3e47e0a9e0e7ebd95601278b66248d66784c75a280b4af4c715","first_computed_at":"2026-07-05T09:39:14.469932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:14.469932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vL1aTdkBDfL5jJxf+xK2YUL0kr/4uEVaO4I8TJfms9r91i9wFunWTujL6bAh2blw5ek91TZ45N/T7ckpITHYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:14.470343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f193f3c726a31b0b9db8b26064e615643d2151697152657761c2807a9210dfb","sha256:d382ddee85ae3e46b290eeae59dbf9bf935814bb32ef35cb7a74233471463416"],"state_sha256":"9f464832743dd2da1fbfa6ac88f0e0f6c281074103181e49fd006043fd9f3f74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1y6vFwv9GATTilSYdO0FIqCQ98H2FlZohIEvuj4S4GA+jvaZOLiBPScbmHwjMpt+ESQrUGplwVt2eLP2xCQ1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:29:38.098940Z","bundle_sha256":"46e073b0ae8834d34b703b1d9dcbee4b020ee2b871bd90e5f0b3d7f6904998b3"}}