{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IP2DPQ2CRRF5EJP3RATFM6VQ2S","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":"6ec27a63e102c022753efe900ceb867019b37c5e9cf47f296ad196e811e6b8a8","cross_cats_sorted":["cs.CE","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-09-20T09:58:20Z","title_canon_sha256":"06a49d58ae67a3ccc38708db3f04c59d0d8b885c4ff93c4d310be3ebdf0f1a72"},"schema_version":"1.0","source":{"id":"1709.06793","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06793","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06793v2","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06793","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"IP2DPQ2CRRF5","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IP2DPQ2CRRF5EJP3","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IP2DPQ2C","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:a2853cd8265c33e08adaaa67575b9551748ed5345d41d5034b614db6fdf13dc8","target":"graph","created_at":"2026-05-18T00:10:11Z","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 novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator that is obtained by appropriately scaling the reference stiffness matrix from the constant coefficient case. Assuming sufficient regularity, an a priori analysis shows that solutions obtained by this approach are unique and have asymptotically optimal order convergence in the $H^1$- and the $L^2$-norm on hierarchical hybrid grids. For the pre-","authors_text":"Barbara Wohlmuth, Christian Waluga, Daniel Drzisga, Marcus Mohr, Simon Bauer, Ulrich Ruede","cross_cats":["cs.CE","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-09-20T09:58:20Z","title":"A stencil scaling approach for accelerating matrix-free finite element implementations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06793","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":"sha256:05b4ef7c0dade9e92e5ee9055db3190a8e1a0264366fc0d56fc710013e8f20d9","target":"record","created_at":"2026-05-18T00:10:11Z","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":"6ec27a63e102c022753efe900ceb867019b37c5e9cf47f296ad196e811e6b8a8","cross_cats_sorted":["cs.CE","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-09-20T09:58:20Z","title_canon_sha256":"06a49d58ae67a3ccc38708db3f04c59d0d8b885c4ff93c4d310be3ebdf0f1a72"},"schema_version":"1.0","source":{"id":"1709.06793","kind":"arxiv","version":2}},"canonical_sha256":"43f437c3428c4bd225fb8826567ab0d4b1d2cd1fd68c1ba5adc2a5eee2bbcbf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43f437c3428c4bd225fb8826567ab0d4b1d2cd1fd68c1ba5adc2a5eee2bbcbf0","first_computed_at":"2026-05-18T00:10:11.348094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:11.348094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xtkf896mZ7e9Mis84dii/mtUEfTfIaiA8oU7L5DncWNotvgjILcXqayoxlNsbgo6jRW2LgtsiXRkEfAohzw3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:11.348625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06793","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05b4ef7c0dade9e92e5ee9055db3190a8e1a0264366fc0d56fc710013e8f20d9","sha256:a2853cd8265c33e08adaaa67575b9551748ed5345d41d5034b614db6fdf13dc8"],"state_sha256":"0ac27254bbdcaf54456d52aa25a04ef530d2f44e9597d70a8f8d0b6e7c0b326f"}