{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GRCUNJ3R3EM5KLIJVTHIMBAJ74","short_pith_number":"pith:GRCUNJ3R","canonical_record":{"source":{"id":"1601.07085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-26T16:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"96b93afeb151b253ed4a08ce6dca85faa946d5432835688141b253f9ddd4341a","abstract_canon_sha256":"6a25cfb3a51dae213f8e51987e7b8758072b43a6533052da94bc6d11505eaf42"},"schema_version":"1.0"},"canonical_sha256":"344546a771d919d52d09acce860409ff02cf1a5e348e2a464a8db95672a88e51","source":{"kind":"arxiv","id":"1601.07085","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07085","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07085v2","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07085","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"GRCUNJ3R3EM5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GRCUNJ3R3EM5KLIJ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GRCUNJ3R","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GRCUNJ3R3EM5KLIJVTHIMBAJ74","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-26T16:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"96b93afeb151b253ed4a08ce6dca85faa946d5432835688141b253f9ddd4341a","abstract_canon_sha256":"6a25cfb3a51dae213f8e51987e7b8758072b43a6533052da94bc6d11505eaf42"},"schema_version":"1.0"},"canonical_sha256":"344546a771d919d52d09acce860409ff02cf1a5e348e2a464a8db95672a88e51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:55.442354Z","signature_b64":"mMQLJeNIpy0LKLBm4Rx3RI3n5QKdnbEJAcCUjCI8k+PPUd3jJRRZcDkwRkIsH9MOmqrIaMZ8N1BJzB3o3DevBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"344546a771d919d52d09acce860409ff02cf1a5e348e2a464a8db95672a88e51","last_reissued_at":"2026-05-18T01:20:55.441726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:55.441726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07085","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tldfGMcvDNjsOAyY5gHvgkLOq3GdhpLmRxxaYQM4tNN+uTeP2WudUhtoLx/I3HswIRXrFNKgfr3Sn5/Q7kMaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:32:30.075006Z"},"content_sha256":"fc3b12f07cbe8f29f058f620cffb54a69f7e37e9fb3a276d6e1a802f0446b7c3","schema_version":"1.0","event_id":"sha256:fc3b12f07cbe8f29f058f620cffb54a69f7e37e9fb3a276d6e1a802f0446b7c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GRCUNJ3R3EM5KLIJVTHIMBAJ74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable and convergent approximation of two-dimensional vector fields on unstructured meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Qingshan Chen","submitted_at":"2016-01-26T16:28:37Z","abstract_excerpt":"A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical schemes through the quantities of vorticity and divergence, instead of individual derivatives of the velocity components. The construction of a stable and convergent external approximation of a simple but relevant vector-valued function space is demonstrated, and the new framework is applied to establish the convergence of the MAC scheme for the incompressib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07085","kind":"arxiv","version":2},"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":"2026-05-18T01:20:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IlZQ41pqo68frpTm4PhumCxvsgxfikcl4MiPQH6yk5VvDrT9qQdllk3An7DYoSubBPY5cz9wOpVmPopBgOnbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:32:30.075366Z"},"content_sha256":"53cb7b2c0595d87011e563f8e71caf38afb14c2873c972765b33041c626a365a","schema_version":"1.0","event_id":"sha256:53cb7b2c0595d87011e563f8e71caf38afb14c2873c972765b33041c626a365a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74/bundle.json","state_url":"https://pith.science/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74/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":"2026-06-20T05:32:30Z","links":{"resolver":"https://pith.science/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74","bundle":"https://pith.science/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74/bundle.json","state":"https://pith.science/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRCUNJ3R3EM5KLIJVTHIMBAJ74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GRCUNJ3R3EM5KLIJVTHIMBAJ74","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":"6a25cfb3a51dae213f8e51987e7b8758072b43a6533052da94bc6d11505eaf42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-26T16:28:37Z","title_canon_sha256":"96b93afeb151b253ed4a08ce6dca85faa946d5432835688141b253f9ddd4341a"},"schema_version":"1.0","source":{"id":"1601.07085","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07085","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07085v2","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07085","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"GRCUNJ3R3EM5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GRCUNJ3R3EM5KLIJ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GRCUNJ3R","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:53cb7b2c0595d87011e563f8e71caf38afb14c2873c972765b33041c626a365a","target":"graph","created_at":"2026-05-18T01:20:55Z","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 new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical schemes through the quantities of vorticity and divergence, instead of individual derivatives of the velocity components. The construction of a stable and convergent external approximation of a simple but relevant vector-valued function space is demonstrated, and the new framework is applied to establish the convergence of the MAC scheme for the incompressib","authors_text":"Qingshan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-26T16:28:37Z","title":"Stable and convergent approximation of two-dimensional vector fields on unstructured meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07085","kind":"arxiv","version":2},"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:fc3b12f07cbe8f29f058f620cffb54a69f7e37e9fb3a276d6e1a802f0446b7c3","target":"record","created_at":"2026-05-18T01:20:55Z","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":"6a25cfb3a51dae213f8e51987e7b8758072b43a6533052da94bc6d11505eaf42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-26T16:28:37Z","title_canon_sha256":"96b93afeb151b253ed4a08ce6dca85faa946d5432835688141b253f9ddd4341a"},"schema_version":"1.0","source":{"id":"1601.07085","kind":"arxiv","version":2}},"canonical_sha256":"344546a771d919d52d09acce860409ff02cf1a5e348e2a464a8db95672a88e51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"344546a771d919d52d09acce860409ff02cf1a5e348e2a464a8db95672a88e51","first_computed_at":"2026-05-18T01:20:55.441726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:55.441726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mMQLJeNIpy0LKLBm4Rx3RI3n5QKdnbEJAcCUjCI8k+PPUd3jJRRZcDkwRkIsH9MOmqrIaMZ8N1BJzB3o3DevBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:55.442354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07085","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc3b12f07cbe8f29f058f620cffb54a69f7e37e9fb3a276d6e1a802f0446b7c3","sha256:53cb7b2c0595d87011e563f8e71caf38afb14c2873c972765b33041c626a365a"],"state_sha256":"8fce8e3d494b0448bde0e06d6537e8108e8002abcd731ce4c28dff0042bd3aa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ow9l3kWkOPpZKLgv+PB0zGEpWoZpo6rBheXSOMYPP5xbVsmveZ06fx/zHswl19srJTC/ZF4N+Js5iUvcyslPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:32:30.077344Z","bundle_sha256":"20fb76eb9c44c80964a199557692f48d1a84460a71a33aff7c13b60af1ef1951"}}