{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:5GEJCOPHM2WEHFS655LRZPIFJR","short_pith_number":"pith:5GEJCOPH","schema_version":"1.0","canonical_sha256":"e9889139e766ac43965eef571cbd054c691d05cfa1f602e94ccb0e43f1ea3d80","source":{"kind":"arxiv","id":"2003.08508","version":3},"attestation_state":"computed","paper":{"title":"An Application of Gaussian Process Modeling for High-order Accurate Adaptive Mesh Refinement Prolongation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Adam Reyes, Carlo Graziani, Dongwook Lee, Petros Tzeferacos, Steven I. Reeves","submitted_at":"2020-03-18T23:39:11Z","abstract_excerpt":"We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the GP methods introduced by A. Reyes et al. (A New Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian Process Modeling, Journal of Scientific Computing, 76 (2017), 443-480; A variable high-order shock-capturing finite difference method with GP-WENO, Jou"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2003.08508","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-03-18T23:39:11Z","cross_cats_sorted":["astro-ph.IM","cs.NA","physics.flu-dyn"],"title_canon_sha256":"4b56ab9bd24a3725116a9540686be4dd0241488547104abea0d9db5f9aa6093e","abstract_canon_sha256":"d352f6d00d04c11656f11aa10f392e3c1eab68d6ef5bb39ace7a471107c5bfc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:05:24.835103Z","signature_b64":"XqfBzaMRl48oiDStSiHWXipoIiYXRKV1API2CijLoJR96+cgHaYk2Ql/UeipDPXZKVr/RrxgundHfFYReWgfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9889139e766ac43965eef571cbd054c691d05cfa1f602e94ccb0e43f1ea3d80","last_reissued_at":"2026-07-05T05:05:24.834635Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:05:24.834635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Application of Gaussian Process Modeling for High-order Accurate Adaptive Mesh Refinement Prolongation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Adam Reyes, Carlo Graziani, Dongwook Lee, Petros Tzeferacos, Steven I. Reeves","submitted_at":"2020-03-18T23:39:11Z","abstract_excerpt":"We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the GP methods introduced by A. Reyes et al. (A New Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian Process Modeling, Journal of Scientific Computing, 76 (2017), 443-480; A variable high-order shock-capturing finite difference method with GP-WENO, Jou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.08508","kind":"arxiv","version":3},"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/2003.08508/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2003.08508","created_at":"2026-07-05T05:05:24.834699+00:00"},{"alias_kind":"arxiv_version","alias_value":"2003.08508v3","created_at":"2026-07-05T05:05:24.834699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.08508","created_at":"2026-07-05T05:05:24.834699+00:00"},{"alias_kind":"pith_short_12","alias_value":"5GEJCOPHM2WE","created_at":"2026-07-05T05:05:24.834699+00:00"},{"alias_kind":"pith_short_16","alias_value":"5GEJCOPHM2WEHFS6","created_at":"2026-07-05T05:05:24.834699+00:00"},{"alias_kind":"pith_short_8","alias_value":"5GEJCOPH","created_at":"2026-07-05T05:05:24.834699+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.03471","citing_title":"GP-Recipe: Gaussian Process approximation to linear operations in numerical methods","ref_index":38,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR","json":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR.json","graph_json":"https://pith.science/api/pith-number/5GEJCOPHM2WEHFS655LRZPIFJR/graph.json","events_json":"https://pith.science/api/pith-number/5GEJCOPHM2WEHFS655LRZPIFJR/events.json","paper":"https://pith.science/paper/5GEJCOPH"},"agent_actions":{"view_html":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR","download_json":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR.json","view_paper":"https://pith.science/paper/5GEJCOPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2003.08508&json=true","fetch_graph":"https://pith.science/api/pith-number/5GEJCOPHM2WEHFS655LRZPIFJR/graph.json","fetch_events":"https://pith.science/api/pith-number/5GEJCOPHM2WEHFS655LRZPIFJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR/action/storage_attestation","attest_author":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR/action/author_attestation","sign_citation":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR/action/citation_signature","submit_replication":"https://pith.science/pith/5GEJCOPHM2WEHFS655LRZPIFJR/action/replication_record"}},"created_at":"2026-07-05T05:05:24.834699+00:00","updated_at":"2026-07-05T05:05:24.834699+00:00"}