{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F4PXW4G7WKXACDELT7KOLBBTUO","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":"905bcb050992c95bdf5023c8fd9dcb9204b4cc0c56a51cd68c936704b6e7b686","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-25T09:53:07Z","title_canon_sha256":"0730b5c2208f5eef17bac6047243f421f2ff0ffa93d597ccf91615f96ec384e6"},"schema_version":"1.0","source":{"id":"1807.09506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09506","created_at":"2026-05-18T00:09:51Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09506v1","created_at":"2026-05-18T00:09:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09506","created_at":"2026-05-18T00:09:51Z"},{"alias_kind":"pith_short_12","alias_value":"F4PXW4G7WKXA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F4PXW4G7WKXACDEL","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F4PXW4G7","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:d3718ade6b8ddd344a10ab3e834582df95578f8be3c36a5f3510a9762527c63d","target":"graph","created_at":"2026-05-18T00:09:51Z","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":"In this article, we extend the Variational Multi-scale method with spectral approximation of the sub-scales to two-dimensional advection-diffusion problems. The spectral VMS method is cast for low-order elements as a standard VMS method with specific stabilized coefficients associated to a component of the advection velocity. We compute the stabilized coefficients for grids of isosceles right triangles and right quadrilaterals, based upon the explicit computation of the eigen-pairs of the advection-diffusion operator with Dirichlet boundary conditions. To reduce the computing time, the stabili","authors_text":"Macarena G\\'omez-M\\'armol, Soledad Fern\\'andez-Garc\\'ia, Tom\\'as Chac\\'on Rebollo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-25T09:53:07Z","title":"VMS spectral solution of two-dimensional advection-diffusion problems with anisotropic velocity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09506","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":"sha256:69a7fbe8c2571cc0ddb0cea0ecbaca5fc7adc5deecf0713ebef7af176688ddcb","target":"record","created_at":"2026-05-18T00:09:51Z","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":"905bcb050992c95bdf5023c8fd9dcb9204b4cc0c56a51cd68c936704b6e7b686","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-25T09:53:07Z","title_canon_sha256":"0730b5c2208f5eef17bac6047243f421f2ff0ffa93d597ccf91615f96ec384e6"},"schema_version":"1.0","source":{"id":"1807.09506","kind":"arxiv","version":1}},"canonical_sha256":"2f1f7b70dfb2ae010c8b9fd4e58433a3b06b01523991a2466b59efef28c253af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f1f7b70dfb2ae010c8b9fd4e58433a3b06b01523991a2466b59efef28c253af","first_computed_at":"2026-05-18T00:09:51.134558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:51.134558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B433DBg6n/69CvwWG8ztSkz8xULl2pqhaRUiUNVbuK8LWQ0ZEdsBzOzdqXsVRxRQDPtJCaNU3NaFncCa324tDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:51.135188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69a7fbe8c2571cc0ddb0cea0ecbaca5fc7adc5deecf0713ebef7af176688ddcb","sha256:d3718ade6b8ddd344a10ab3e834582df95578f8be3c36a5f3510a9762527c63d"],"state_sha256":"83b2d7396ea69968c8a5912a298fdedfa23ad448daa35e8161704c9313e83cf3"}