{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WQQIR4FQLYDWQD4YVKMG2YKVYN","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":"8302b7f98d16a074d63cac611ef50476dfbbb0bf68c86d7fe89573164e98012a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T17:22:51Z","title_canon_sha256":"1022b3540ed21effd5d1c56579511fc2eda81ac0cbf77bed0e91b0234f67270b"},"schema_version":"1.0","source":{"id":"1201.3564","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3564","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3564v3","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3564","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"WQQIR4FQLYDW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WQQIR4FQLYDWQD4Y","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WQQIR4FQ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:4859e94b3b8127d727c00fbac7dc73561f0e943ba52631f36d6a0b0c9e54a51c","target":"graph","created_at":"2026-05-18T02:49:20Z","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":"A mesh condition is developed for linear finite element approximations of anisotropic diffusion-convection-reaction problems to satisfy a discrete maximum principle. Loosely speaking, the condition requires that the mesh be simplicial and $\\mathcal{O}(\\|\\V{b}\\|_\\infty h + \\|c\\|_\\infty h^2)$-nonobtuse when the dihedral angles are measured in the metric specified by the inverse of the diffusion matrix, where $h$ denotes the mesh size and $\\V{b}$ and $c$ are the coefficients of the convection and reaction terms. In two dimensions, the condition can be replaced by a weaker mesh condition (an $\\mat","authors_text":"Changna Lu, Jianxian Qiu, Weizhang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T17:22:51Z","title":"Maximum principle in linear finite element approximations of anisotropic diffusion-convection-reaction problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3564","kind":"arxiv","version":3},"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:cb9a9cbaa6bd38e66c8d0772bc14dade0511b2d3e4740da2459c23d2a229bc14","target":"record","created_at":"2026-05-18T02:49:20Z","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":"8302b7f98d16a074d63cac611ef50476dfbbb0bf68c86d7fe89573164e98012a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T17:22:51Z","title_canon_sha256":"1022b3540ed21effd5d1c56579511fc2eda81ac0cbf77bed0e91b0234f67270b"},"schema_version":"1.0","source":{"id":"1201.3564","kind":"arxiv","version":3}},"canonical_sha256":"b42088f0b05e07680f98aa986d6155c36ab4150d017356c39fefca0f823731c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b42088f0b05e07680f98aa986d6155c36ab4150d017356c39fefca0f823731c4","first_computed_at":"2026-05-18T02:49:20.617179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:20.617179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dl5uQHVxGDgNp+Xrip12LnwujtbZLQJf2VQeOPLwoZv36eD3OCxPOCPd+CJjMZEHcI/lnwTvhgRjbC/rgUelBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:20.617838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3564","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb9a9cbaa6bd38e66c8d0772bc14dade0511b2d3e4740da2459c23d2a229bc14","sha256:4859e94b3b8127d727c00fbac7dc73561f0e943ba52631f36d6a0b0c9e54a51c"],"state_sha256":"31c2a77c7b19c2292833e0777f1fe1ad89938ec0edbc429735cf228092435062"}