{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2QJMHK72P6UBTYMQJWJURJO5EN","short_pith_number":"pith:2QJMHK72","canonical_record":{"source":{"id":"1509.02615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-09-09T02:43:38Z","cross_cats_sorted":["math.NA","physics.ao-ph"],"title_canon_sha256":"b400bcb9586799d61806ed72e1e57712fde0c4dce1b0c90bfc2b431cfcaabc59","abstract_canon_sha256":"d1a81a9fe18ea382b7953311c27d812a1fe507849992f0242a62cf2f1beedbbe"},"schema_version":"1.0"},"canonical_sha256":"d412c3abfa7fa819e1904d9348a5dd2372f24fae875be6f6ae13b4eac7510b41","source":{"kind":"arxiv","id":"1509.02615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02615","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02615v1","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02615","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"2QJMHK72P6UB","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QJMHK72P6UBTYMQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QJMHK72","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2QJMHK72P6UBTYMQJWJURJO5EN","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-09-09T02:43:38Z","cross_cats_sorted":["math.NA","physics.ao-ph"],"title_canon_sha256":"b400bcb9586799d61806ed72e1e57712fde0c4dce1b0c90bfc2b431cfcaabc59","abstract_canon_sha256":"d1a81a9fe18ea382b7953311c27d812a1fe507849992f0242a62cf2f1beedbbe"},"schema_version":"1.0"},"canonical_sha256":"d412c3abfa7fa819e1904d9348a5dd2372f24fae875be6f6ae13b4eac7510b41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:34.565201Z","signature_b64":"Gy5mBQE2ZBN5KiuGNo+yqKpNgWna3ZDVZCW3pamyfO/W5M+BMZrJr1ZQgeFFFk48N8C0D6cehDT+Il0uPykbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d412c3abfa7fa819e1904d9348a5dd2372f24fae875be6f6ae13b4eac7510b41","last_reissued_at":"2026-05-18T01:33:34.564515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:34.564515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02615","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":"2026-05-18T01:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F3qWHTQuSIwuNeiR5ae/kTq9DCHuD8wWx+hpOJodsclKE3eXx0oxuVGRAStxjugRfAR8nGU7xbFhZqd7ujMtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:45:18.811258Z"},"content_sha256":"5b3bdeefea8672c84ef2416d96ac59ec593f90a1946a9a05155b46234204cdb3","schema_version":"1.0","event_id":"sha256:5b3bdeefea8672c84ef2416d96ac59ec593f90a1946a9a05155b46234204cdb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2QJMHK72P6UBTYMQJWJURJO5EN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An RBF-FD polynomial method based on polyharmonic splines for the Navier-Stokes equations: Comparisons on different node layouts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.ao-ph"],"primary_cat":"physics.comp-ph","authors_text":"Gregory A. Barnett, Louis J. Wicker, Natasha Flyer","submitted_at":"2015-09-09T02:43:38Z","abstract_excerpt":"Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for the presented approach. Comparisons are done on Cartesian, hexagonal, and quasi-uniformly s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02615","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":""},"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":"2026-05-18T01:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wa5KKTssCCKa0F//cDZVr9BUTQl/DalIWXQ5ECsMqCofRrBa95V4g3xurkXYHKeuAb6vdpWdt1Luh+8QdW6mDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:45:18.812000Z"},"content_sha256":"562e45b5ddd80290dcf276712cbcb606f0564bbfa85e04209aff6dad6cbd0488","schema_version":"1.0","event_id":"sha256:562e45b5ddd80290dcf276712cbcb606f0564bbfa85e04209aff6dad6cbd0488"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QJMHK72P6UBTYMQJWJURJO5EN/bundle.json","state_url":"https://pith.science/pith/2QJMHK72P6UBTYMQJWJURJO5EN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QJMHK72P6UBTYMQJWJURJO5EN/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":"2026-06-25T17:45:18Z","links":{"resolver":"https://pith.science/pith/2QJMHK72P6UBTYMQJWJURJO5EN","bundle":"https://pith.science/pith/2QJMHK72P6UBTYMQJWJURJO5EN/bundle.json","state":"https://pith.science/pith/2QJMHK72P6UBTYMQJWJURJO5EN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QJMHK72P6UBTYMQJWJURJO5EN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2QJMHK72P6UBTYMQJWJURJO5EN","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":"d1a81a9fe18ea382b7953311c27d812a1fe507849992f0242a62cf2f1beedbbe","cross_cats_sorted":["math.NA","physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-09-09T02:43:38Z","title_canon_sha256":"b400bcb9586799d61806ed72e1e57712fde0c4dce1b0c90bfc2b431cfcaabc59"},"schema_version":"1.0","source":{"id":"1509.02615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02615","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02615v1","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02615","created_at":"2026-05-18T01:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"2QJMHK72P6UB","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2QJMHK72P6UBTYMQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2QJMHK72","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:562e45b5ddd80290dcf276712cbcb606f0564bbfa85e04209aff6dad6cbd0488","target":"graph","created_at":"2026-05-18T01:33:34Z","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"},"paper":{"abstract_excerpt":"Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for the presented approach. Comparisons are done on Cartesian, hexagonal, and quasi-uniformly s","authors_text":"Gregory A. Barnett, Louis J. Wicker, Natasha Flyer","cross_cats":["math.NA","physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-09-09T02:43:38Z","title":"An RBF-FD polynomial method based on polyharmonic splines for the Navier-Stokes equations: Comparisons on different node layouts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02615","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":"sha256:5b3bdeefea8672c84ef2416d96ac59ec593f90a1946a9a05155b46234204cdb3","target":"record","created_at":"2026-05-18T01:33:34Z","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":"d1a81a9fe18ea382b7953311c27d812a1fe507849992f0242a62cf2f1beedbbe","cross_cats_sorted":["math.NA","physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-09-09T02:43:38Z","title_canon_sha256":"b400bcb9586799d61806ed72e1e57712fde0c4dce1b0c90bfc2b431cfcaabc59"},"schema_version":"1.0","source":{"id":"1509.02615","kind":"arxiv","version":1}},"canonical_sha256":"d412c3abfa7fa819e1904d9348a5dd2372f24fae875be6f6ae13b4eac7510b41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d412c3abfa7fa819e1904d9348a5dd2372f24fae875be6f6ae13b4eac7510b41","first_computed_at":"2026-05-18T01:33:34.564515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:34.564515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gy5mBQE2ZBN5KiuGNo+yqKpNgWna3ZDVZCW3pamyfO/W5M+BMZrJr1ZQgeFFFk48N8C0D6cehDT+Il0uPykbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:34.565201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b3bdeefea8672c84ef2416d96ac59ec593f90a1946a9a05155b46234204cdb3","sha256:562e45b5ddd80290dcf276712cbcb606f0564bbfa85e04209aff6dad6cbd0488"],"state_sha256":"fbf801f0a71a51b5b625960e386df371895d883a407bbb12f86bfa1edd2c43c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJc21NK2w09VpPdTbKSq0lONvnxxokaESCgTxYyEf030cjzVxSeJezeFzMBjaPJlDBIjB87JXgihtWWvTzwEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:45:18.814240Z","bundle_sha256":"14def4cbaac95400e678f96e65935b0a0bd9402f9dd84399d0f406374c063ec0"}}