{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YVBC6TMP6JMCZGTADMEXKCTMW3","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":"b248cf082bbc5a5a01a2729c0585e73a414bf36b764029c9eb7348cb34aed6b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-03T21:24:00Z","title_canon_sha256":"da6cb92638584c11df5f6bbaa3c65e23985e1e0d6a33fcd7de6ba164b04cbd4c"},"schema_version":"1.0","source":{"id":"1101.0612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0612","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0612v1","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0612","created_at":"2026-05-18T03:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"YVBC6TMP6JMC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YVBC6TMP6JMCZGTA","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YVBC6TMP","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:cf69b8d130bf08cfafede90a9b02165de52453534ae4da679ecffce85b9ed92d","target":"graph","created_at":"2026-05-18T03:54:16Z","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":"Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the Lp norm and we consider Lagrange finite elements of arbitrary polynomial degree m-1. We establish sharp asymptotic error estimates as N tends to infinity when the optimal anisotropic triangulation is used, recovering the earlier results on piecewise linear interpolation, an improving the resu","authors_text":"Jean-Marie Mirebeau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-03T21:24:00Z","title":"Optimal Meshes for Finite Elements of Arbitrary Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0612","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:d1bf0001dfdb84de6f56385cb79bf65c2ed314ea20e94619445152c478714dad","target":"record","created_at":"2026-05-18T03:54:16Z","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":"b248cf082bbc5a5a01a2729c0585e73a414bf36b764029c9eb7348cb34aed6b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-03T21:24:00Z","title_canon_sha256":"da6cb92638584c11df5f6bbaa3c65e23985e1e0d6a33fcd7de6ba164b04cbd4c"},"schema_version":"1.0","source":{"id":"1101.0612","kind":"arxiv","version":1}},"canonical_sha256":"c5422f4d8ff2582c9a601b09750a6cb6c2cc3173ccd399fc323745069249a7b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5422f4d8ff2582c9a601b09750a6cb6c2cc3173ccd399fc323745069249a7b9","first_computed_at":"2026-05-18T03:54:16.010196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:16.010196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EJfrcI6Okv5y14pxcYL6f+Z+SdDBSOwqwEJdnCCztufuyv9+29+TD4XqYx5mondWvZiLZMjPjI6UFebnql3vCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:16.010654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1bf0001dfdb84de6f56385cb79bf65c2ed314ea20e94619445152c478714dad","sha256:cf69b8d130bf08cfafede90a9b02165de52453534ae4da679ecffce85b9ed92d"],"state_sha256":"eec2c6ea1ce79f0383d0f8b5b1745533a44595fe8c49b98925463be6693153bf"}