{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4EWCJ37MMSXIRGCHZC5LU3PZM6","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":"d78392c979474743392c77e05cf2a4891537dea7d3cb392531dd4881f5173c8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T11:27:53Z","title_canon_sha256":"ce83e631db6430e734b8b76ef86f422d5a4b74f3593d32c6a6ec3efb459751d6"},"schema_version":"1.0","source":{"id":"1711.04274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04274","created_at":"2026-05-18T00:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04274v2","created_at":"2026-05-18T00:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04274","created_at":"2026-05-18T00:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"4EWCJ37MMSXI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4EWCJ37MMSXIRGCH","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4EWCJ37M","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:9d5e09bdc72b8a01e901210cbba207176dcc8bc2470f9ebb87ab8cd5c13c6986","target":"graph","created_at":"2026-05-18T00:16:30Z","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":"We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators.\n  The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty meth","authors_text":"Juha Videman, K. R. Rajagopal, Rolf Stenberg, Tom Gustafsson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T11:27:53Z","title":"An adaptive finite element method for the inequality-constrained Reynolds equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04274","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":"sha256:45e08558111c919f60473ee5ed76a27e61f907155f73545ea27795cc0b241124","target":"record","created_at":"2026-05-18T00:16:30Z","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":"d78392c979474743392c77e05cf2a4891537dea7d3cb392531dd4881f5173c8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T11:27:53Z","title_canon_sha256":"ce83e631db6430e734b8b76ef86f422d5a4b74f3593d32c6a6ec3efb459751d6"},"schema_version":"1.0","source":{"id":"1711.04274","kind":"arxiv","version":2}},"canonical_sha256":"e12c24efec64ae889847c8baba6df967a2d9dbb86852a44587dd7d01d191b7ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e12c24efec64ae889847c8baba6df967a2d9dbb86852a44587dd7d01d191b7ae","first_computed_at":"2026-05-18T00:16:30.499337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:30.499337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOnf791Pf8LWJWmfy3nqqUVFC1iGYqb5mHtPgREFMs66XSk/4uX7JjnzdIkj0M1M4hTsvGT+CIfrX1HrNcOrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:30.499772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45e08558111c919f60473ee5ed76a27e61f907155f73545ea27795cc0b241124","sha256:9d5e09bdc72b8a01e901210cbba207176dcc8bc2470f9ebb87ab8cd5c13c6986"],"state_sha256":"576736e8b7b1404cc424dd7749684fd5182765f61ee56e5e34ebb69b456a5e7f"}