{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:42WNRHFVMX7NGWZBPK3BSNZH6M","short_pith_number":"pith:42WNRHFV","canonical_record":{"source":{"id":"1611.03911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-11T23:37:30Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"837221ceb9918e59fc8b2fa9e1f604e75e88d10308da339e5cbd66423ac7a012","abstract_canon_sha256":"50ce849194c48bc80f43a9698deb16559f65320a81ffce5a0035eea094d8f467"},"schema_version":"1.0"},"canonical_sha256":"e6acd89cb565fed35b217ab6193727f30e8f571bbcd07bf4cddc4bf835f48e30","source":{"kind":"arxiv","id":"1611.03911","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03911","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03911v1","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03911","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"42WNRHFVMX7N","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"42WNRHFVMX7NGWZB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"42WNRHFV","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:42WNRHFVMX7NGWZBPK3BSNZH6M","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-11T23:37:30Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"837221ceb9918e59fc8b2fa9e1f604e75e88d10308da339e5cbd66423ac7a012","abstract_canon_sha256":"50ce849194c48bc80f43a9698deb16559f65320a81ffce5a0035eea094d8f467"},"schema_version":"1.0"},"canonical_sha256":"e6acd89cb565fed35b217ab6193727f30e8f571bbcd07bf4cddc4bf835f48e30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:18.097044Z","signature_b64":"3ITLJrJ067AjHkLO5xj7XRFQu0qauOqykhxwntMY2tEChn+HFk1fgAopUcw2ZEB4fW+B6UqnP2K1/kFo+EiSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6acd89cb565fed35b217ab6193727f30e8f571bbcd07bf4cddc4bf835f48e30","last_reissued_at":"2026-05-18T00:59:18.096340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:18.096340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03911","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":"2026-05-18T00:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eStPYZfw4LCK2vIX6U2pcndBetl734O+Y7vCjR4bH21ueWUw1LPomXHUVpV2PFA83SgqbPduG34KLCNx2+bBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:44:50.275803Z"},"content_sha256":"7ecfbb62f44eabbe2ca8052c9fe1ac569a59914bdeeb32351aa4bfaa72b9aaf4","schema_version":"1.0","event_id":"sha256:7ecfbb62f44eabbe2ca8052c9fe1ac569a59914bdeeb32351aa4bfaa72b9aaf4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:42WNRHFVMX7NGWZBPK3BSNZH6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A compatible high-order meshless method for the Stokes equations with applications to suspension flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"math.NA","authors_text":"Martin Maxey, Nathaniel Trask, Xiaozhe Hu","submitted_at":"2016-11-11T23:37:30Z","abstract_excerpt":"A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03911","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":"2026-05-18T00:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UKBdDWDlbvqpt5O3O/0SY0z/ZWNQCP5kaEHxgjlOvpaWyUvZ+uetaMCtsuqQkftst2pgR8g9cYvxmJQ6mqvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:44:50.276136Z"},"content_sha256":"2b745df0bdc68879b898d9bdaff22e98827ea627f8ff074f3af196853ff54986","schema_version":"1.0","event_id":"sha256:2b745df0bdc68879b898d9bdaff22e98827ea627f8ff074f3af196853ff54986"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42WNRHFVMX7NGWZBPK3BSNZH6M/bundle.json","state_url":"https://pith.science/pith/42WNRHFVMX7NGWZBPK3BSNZH6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42WNRHFVMX7NGWZBPK3BSNZH6M/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":"2026-06-09T09:44:50Z","links":{"resolver":"https://pith.science/pith/42WNRHFVMX7NGWZBPK3BSNZH6M","bundle":"https://pith.science/pith/42WNRHFVMX7NGWZBPK3BSNZH6M/bundle.json","state":"https://pith.science/pith/42WNRHFVMX7NGWZBPK3BSNZH6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42WNRHFVMX7NGWZBPK3BSNZH6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:42WNRHFVMX7NGWZBPK3BSNZH6M","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":"50ce849194c48bc80f43a9698deb16559f65320a81ffce5a0035eea094d8f467","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-11T23:37:30Z","title_canon_sha256":"837221ceb9918e59fc8b2fa9e1f604e75e88d10308da339e5cbd66423ac7a012"},"schema_version":"1.0","source":{"id":"1611.03911","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03911","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03911v1","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03911","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"42WNRHFVMX7N","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"42WNRHFVMX7NGWZB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"42WNRHFV","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:2b745df0bdc68879b898d9bdaff22e98827ea627f8ff074f3af196853ff54986","target":"graph","created_at":"2026-05-18T00:59:18Z","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":"A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure","authors_text":"Martin Maxey, Nathaniel Trask, Xiaozhe Hu","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-11T23:37:30Z","title":"A compatible high-order meshless method for the Stokes equations with applications to suspension flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03911","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":"sha256:7ecfbb62f44eabbe2ca8052c9fe1ac569a59914bdeeb32351aa4bfaa72b9aaf4","target":"record","created_at":"2026-05-18T00:59:18Z","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":"50ce849194c48bc80f43a9698deb16559f65320a81ffce5a0035eea094d8f467","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-11T23:37:30Z","title_canon_sha256":"837221ceb9918e59fc8b2fa9e1f604e75e88d10308da339e5cbd66423ac7a012"},"schema_version":"1.0","source":{"id":"1611.03911","kind":"arxiv","version":1}},"canonical_sha256":"e6acd89cb565fed35b217ab6193727f30e8f571bbcd07bf4cddc4bf835f48e30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6acd89cb565fed35b217ab6193727f30e8f571bbcd07bf4cddc4bf835f48e30","first_computed_at":"2026-05-18T00:59:18.096340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:18.096340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ITLJrJ067AjHkLO5xj7XRFQu0qauOqykhxwntMY2tEChn+HFk1fgAopUcw2ZEB4fW+B6UqnP2K1/kFo+EiSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:18.097044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03911","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ecfbb62f44eabbe2ca8052c9fe1ac569a59914bdeeb32351aa4bfaa72b9aaf4","sha256:2b745df0bdc68879b898d9bdaff22e98827ea627f8ff074f3af196853ff54986"],"state_sha256":"74c1c632663698a733c607309bdab55bab5084d6bb79b69895e8a66243b75d9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y70MkYIsIMRu5gcZTDtC8QToltff1aFooIhuDSIJHBBX6Od8mpo8LC3a5cNSKrWHR9d+j5adBSUCsa6bBLEoDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:44:50.278122Z","bundle_sha256":"dcee660d900aa5c4d627d2624abd3a45a1d1139cfe96c311a0af0fc257e5a128"}}