{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XP56QGTCKF4JBQH5Y5LUH242EH","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":"c985b44703a1e3544e521f4924bd4806d1c55280cb3bbb9f5efa1a3a318ae84e","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T20:40:34Z","title_canon_sha256":"68542b3f4b9ae404edf519881de81caae682a0e31ca0b3c56179d43a021c89cf"},"schema_version":"1.0","source":{"id":"1410.0045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0045","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0045v1","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0045","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"XP56QGTCKF4J","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XP56QGTCKF4JBQH5","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XP56QGTC","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:57c7e00d0473120218c48b7177d0eb46208b968d80c361c48750c403e777053f","target":"graph","created_at":"2026-05-18T02:41:18Z","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":"We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and converge","authors_text":"Colin J. Cotter, Robert C. Kirby","cross_cats":["physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T20:40:34Z","title":"Mixed finite elements for global tide models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0045","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":"sha256:0c7e016f5a7a4aafbd70792282d3da3e59e0a8af1d9e8403721e166638b9ddcc","target":"record","created_at":"2026-05-18T02:41:18Z","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":"c985b44703a1e3544e521f4924bd4806d1c55280cb3bbb9f5efa1a3a318ae84e","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-30T20:40:34Z","title_canon_sha256":"68542b3f4b9ae404edf519881de81caae682a0e31ca0b3c56179d43a021c89cf"},"schema_version":"1.0","source":{"id":"1410.0045","kind":"arxiv","version":1}},"canonical_sha256":"bbfbe81a62517890c0fdc75743eb9a21defe629e4f3919a73eb8e1ee866e49d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbfbe81a62517890c0fdc75743eb9a21defe629e4f3919a73eb8e1ee866e49d1","first_computed_at":"2026-05-18T02:41:18.147538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:18.147538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GRD44v0VILqp7Yhgo4QEmz1nItXADZQuJjW/1E1IRwZADpQEDJTOr1MTBPMyJ3P5j8U0QkZJ7qCkXfljalacCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:18.147974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c7e016f5a7a4aafbd70792282d3da3e59e0a8af1d9e8403721e166638b9ddcc","sha256:57c7e00d0473120218c48b7177d0eb46208b968d80c361c48750c403e777053f"],"state_sha256":"2a917d0c2dd2ff70da81d98baf36d2a7054a106ba7907dfedde687be622c0b25"}