{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VP7GDWDVOYUHHESQK5TWXA5HSJ","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":"aade134b9ffb7416369273c7df83803ed544bd97aa66c29dc7d5bbfd2cee8091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-07-23T13:46:33Z","title_canon_sha256":"5a5c2aa9e977c46dd5c23483025b831ee7a9dd9abfffd502f53ea33815fe1cc7"},"schema_version":"1.0","source":{"id":"0907.4066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4066","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4066v2","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4066","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"VP7GDWDVOYUH","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VP7GDWDVOYUHHESQ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VP7GDWDV","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:57d751b8642b22246693afe11ec12a2f74803a458bee10e78b45691206d3ea88","target":"graph","created_at":"2026-05-18T00:14:57Z","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":"Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are aproximated by either (a) piecewise constants or (b) continuous piecewise linears, the velocity by (a) continuous piecewise quadratics or a reduced version with linear tangential component on each edge, and (b) by continuous piecewise quadratics or the mini-element. Both schemes (a) and (b) satisfy a free energy bound, which involves the logarithm of the conformatio","authors_text":"John W. Barrett, Sebastien Boyaval","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-07-23T13:46:33Z","title":"Existence and approximation of a (regularized) Oldroyd-B model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4066","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:d7fbde5fdf87c8c6b77113cb3553bed62b24edd992801ff6d373ca8dfa9c4a63","target":"record","created_at":"2026-05-18T00:14:57Z","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":"aade134b9ffb7416369273c7df83803ed544bd97aa66c29dc7d5bbfd2cee8091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-07-23T13:46:33Z","title_canon_sha256":"5a5c2aa9e977c46dd5c23483025b831ee7a9dd9abfffd502f53ea33815fe1cc7"},"schema_version":"1.0","source":{"id":"0907.4066","kind":"arxiv","version":2}},"canonical_sha256":"abfe61d875762873925057676b83a7926fb476a5a45fec910fb2b0ebffd9aac3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abfe61d875762873925057676b83a7926fb476a5a45fec910fb2b0ebffd9aac3","first_computed_at":"2026-05-18T00:14:57.756714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:57.756714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mnvRxhn4wdaxbnzmTl4O4aurARzOEplIiOU4GXJpFt5SjkyYolKaSG3dlLHJXbpDObhFWjYQrK7rnOWztHLcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:57.757418Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7fbde5fdf87c8c6b77113cb3553bed62b24edd992801ff6d373ca8dfa9c4a63","sha256:57d751b8642b22246693afe11ec12a2f74803a458bee10e78b45691206d3ea88"],"state_sha256":"ecdd726f409d649ffd961456ea56284753f23f0ecdad4e74774a7800ab7cfb1f"}