{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DO3QANYRXJ4TL653LQI7WMA7BS","short_pith_number":"pith:DO3QANYR","canonical_record":{"source":{"id":"1505.06931","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T13:00:32Z","cross_cats_sorted":[],"title_canon_sha256":"8a068132015311f18664ca2c24bfb2a13448ef9cfb93db4914087b2a1edc41e0","abstract_canon_sha256":"71c70b783b21bbb562d3636c9210372bdff8e8b4831ac6fdd85da872807c29a8"},"schema_version":"1.0"},"canonical_sha256":"1bb7003711ba7935fbbb5c11fb301f0cb339eb4e381e9ea1f57325b36b8e25a8","source":{"kind":"arxiv","id":"1505.06931","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06931","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06931v4","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06931","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"DO3QANYRXJ4T","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DO3QANYRXJ4TL653","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DO3QANYR","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DO3QANYRXJ4TL653LQI7WMA7BS","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06931","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T13:00:32Z","cross_cats_sorted":[],"title_canon_sha256":"8a068132015311f18664ca2c24bfb2a13448ef9cfb93db4914087b2a1edc41e0","abstract_canon_sha256":"71c70b783b21bbb562d3636c9210372bdff8e8b4831ac6fdd85da872807c29a8"},"schema_version":"1.0"},"canonical_sha256":"1bb7003711ba7935fbbb5c11fb301f0cb339eb4e381e9ea1f57325b36b8e25a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:06.526603Z","signature_b64":"r2kYP5nCMKISMllnqzEqt2ckVT/ROd8um1sPfZARYQ5OgDqEqYnr3kC8or+cCu8eSo9BmXzdbM3neBT6Z7OjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bb7003711ba7935fbbb5c11fb301f0cb339eb4e381e9ea1f57325b36b8e25a8","last_reissued_at":"2026-05-18T01:03:06.526125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:06.526125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06931","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cC2dHXG0dqkreFKGKwuE1yQNMQ3aPal1OJ5awyE0g3Ww83r6mVBvNRfGkJp72IDHSwCyUNIa9TpTCalFyXTzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:09:53.739979Z"},"content_sha256":"f965a7fd4d8c5efdd380b95c044910ea06402043716bd4111f5ba6af8c4a727a","schema_version":"1.0","event_id":"sha256:f965a7fd4d8c5efdd380b95c044910ea06402043716bd4111f5ba6af8c4a727a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DO3QANYRXJ4TL653LQI7WMA7BS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite element quasi-interpolation and best approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexandre Ern, Jean-Luc Guermond","submitted_at":"2015-05-26T13:00:32Z","abstract_excerpt":"This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the best approximation error in any $L^p$-norm assuming regularity in the fractional Sobolev spaces $W^{r,p}$, where $p\\in [1,\\infty]$ and the smoothness index $r$ can be arbitrarily close to zero. The operator is stable in $L^1$, leaves the corresponding finite element space point-wise invariant whether homogeneous boundary conditions are imposed or not. The theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06931","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jqypnu/dd6WwRgg62xj0rd21din3jBIkFPxxgCdqCV9Ht54qT2WpgR3KqXZPniNuG7IHGGnpfPofflSRcf82BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:09:53.740657Z"},"content_sha256":"df11978a8888eae580dffdeaf9aa36b455aaee64f379af7bfa36c27fd69088b3","schema_version":"1.0","event_id":"sha256:df11978a8888eae580dffdeaf9aa36b455aaee64f379af7bfa36c27fd69088b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DO3QANYRXJ4TL653LQI7WMA7BS/bundle.json","state_url":"https://pith.science/pith/DO3QANYRXJ4TL653LQI7WMA7BS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DO3QANYRXJ4TL653LQI7WMA7BS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T17:09:53Z","links":{"resolver":"https://pith.science/pith/DO3QANYRXJ4TL653LQI7WMA7BS","bundle":"https://pith.science/pith/DO3QANYRXJ4TL653LQI7WMA7BS/bundle.json","state":"https://pith.science/pith/DO3QANYRXJ4TL653LQI7WMA7BS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DO3QANYRXJ4TL653LQI7WMA7BS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DO3QANYRXJ4TL653LQI7WMA7BS","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":"71c70b783b21bbb562d3636c9210372bdff8e8b4831ac6fdd85da872807c29a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T13:00:32Z","title_canon_sha256":"8a068132015311f18664ca2c24bfb2a13448ef9cfb93db4914087b2a1edc41e0"},"schema_version":"1.0","source":{"id":"1505.06931","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06931","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06931v4","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06931","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"DO3QANYRXJ4T","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DO3QANYRXJ4TL653","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DO3QANYR","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:df11978a8888eae580dffdeaf9aa36b455aaee64f379af7bfa36c27fd69088b3","target":"graph","created_at":"2026-05-18T01:03:06Z","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":"This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the best approximation error in any $L^p$-norm assuming regularity in the fractional Sobolev spaces $W^{r,p}$, where $p\\in [1,\\infty]$ and the smoothness index $r$ can be arbitrarily close to zero. The operator is stable in $L^1$, leaves the corresponding finite element space point-wise invariant whether homogeneous boundary conditions are imposed or not. The theo","authors_text":"Alexandre Ern, Jean-Luc Guermond","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T13:00:32Z","title":"Finite element quasi-interpolation and best approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06931","kind":"arxiv","version":4},"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:f965a7fd4d8c5efdd380b95c044910ea06402043716bd4111f5ba6af8c4a727a","target":"record","created_at":"2026-05-18T01:03:06Z","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":"71c70b783b21bbb562d3636c9210372bdff8e8b4831ac6fdd85da872807c29a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-26T13:00:32Z","title_canon_sha256":"8a068132015311f18664ca2c24bfb2a13448ef9cfb93db4914087b2a1edc41e0"},"schema_version":"1.0","source":{"id":"1505.06931","kind":"arxiv","version":4}},"canonical_sha256":"1bb7003711ba7935fbbb5c11fb301f0cb339eb4e381e9ea1f57325b36b8e25a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bb7003711ba7935fbbb5c11fb301f0cb339eb4e381e9ea1f57325b36b8e25a8","first_computed_at":"2026-05-18T01:03:06.526125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:06.526125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2kYP5nCMKISMllnqzEqt2ckVT/ROd8um1sPfZARYQ5OgDqEqYnr3kC8or+cCu8eSo9BmXzdbM3neBT6Z7OjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:06.526603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06931","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f965a7fd4d8c5efdd380b95c044910ea06402043716bd4111f5ba6af8c4a727a","sha256:df11978a8888eae580dffdeaf9aa36b455aaee64f379af7bfa36c27fd69088b3"],"state_sha256":"3b731ae7e5941fdbfe075d67b728595dc692c9ee52e46182ba1aa56b0fa5b7dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"45USmxR0hyYqylLZb1jMp+cCFw0wSvRmGe8eQ7RNM1D0ycz0UOpluTDYR6e+aRCUoX+fR0Lq3QORTkeW4cLmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:09:53.744294Z","bundle_sha256":"287be33cb66c4528c52c7dec95ee00d83a7f37b9e63439f581b351dcd004bbbb"}}