{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R32RAQVOQUKPL7MBVAUDYR3LTN","short_pith_number":"pith:R32RAQVO","canonical_record":{"source":{"id":"1606.02832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-09T06:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"2de6c43b28a1eab11312244908b8e1d8ecd41bdc05c301a9253f67a75ae33d12","abstract_canon_sha256":"8a0a32e9a7a26f9c0c4d0594936f5e6d75891eb68a04b8f8780a56eb88cd2c81"},"schema_version":"1.0"},"canonical_sha256":"8ef51042ae8514f5fd81a8283c476b9b7551bb949cd2fd2ab421f7f7340c60d0","source":{"kind":"arxiv","id":"1606.02832","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02832","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02832v2","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02832","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"R32RAQVOQUKP","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R32RAQVOQUKPL7MB","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R32RAQVO","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R32RAQVOQUKPL7MBVAUDYR3LTN","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-09T06:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"2de6c43b28a1eab11312244908b8e1d8ecd41bdc05c301a9253f67a75ae33d12","abstract_canon_sha256":"8a0a32e9a7a26f9c0c4d0594936f5e6d75891eb68a04b8f8780a56eb88cd2c81"},"schema_version":"1.0"},"canonical_sha256":"8ef51042ae8514f5fd81a8283c476b9b7551bb949cd2fd2ab421f7f7340c60d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:24.595498Z","signature_b64":"0lZemjYHfSWhRl//WyoNg6c0/M9pP3YzfI75XbC1M5WDC598W6ZFa3Nf6pO74RQs3a11AY4lFtVYG+my8A2hBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ef51042ae8514f5fd81a8283c476b9b7551bb949cd2fd2ab421f7f7340c60d0","last_reissued_at":"2026-05-18T00:49:24.594798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:24.594798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02832","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Wgg509mtX4j+mdASqpAo8SfDh6EU77nMZdDf/olcHfKbREoParGDTkup4ckHePlWwDrzXvSSE751xjWQ6zaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:54:37.633523Z"},"content_sha256":"7378ba7d767a5ae915ca80df82b7f6f537751efabeab2984ea3840e9718f0382","schema_version":"1.0","event_id":"sha256:7378ba7d767a5ae915ca80df82b7f6f537751efabeab2984ea3840e9718f0382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R32RAQVOQUKPL7MBVAUDYR3LTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$W^{s,p}$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Daniele Di Pietro, Jerome Droniou","submitted_at":"2016-06-09T06:27:30Z","abstract_excerpt":"In this work we prove optimal $W^{s,p}$-approximation estimates (with $p\\in[1,+\\infty]$) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont--Scott approximation theory together with two novel abstract lemmas: An approximation result for bounded projectors, and an $L^p$-boundedness result for $L^2$-orthogonal projectors on polynomial subspaces. The $W^{s,p}$-approximation results have general applicability to (standard or polytopal) numerical methods based on local polynomial spaces. As an illustration, we use these $W^{s,p}$-estimates to derive novel e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02832","kind":"arxiv","version":2},"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":"2026-05-18T00:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZeHuDB7JiP3XmSj+IIcZ8dQg+DDXDizCPy/WWQHnFqB2Nmnni3WKPumgKJrrdJU6SUKcGDWp4ZIBHqqRKQmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:54:37.633904Z"},"content_sha256":"ebd036a9ed8aa54a07133ec8911b77f552cb40724444a8b1f8124d437436bd9f","schema_version":"1.0","event_id":"sha256:ebd036a9ed8aa54a07133ec8911b77f552cb40724444a8b1f8124d437436bd9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R32RAQVOQUKPL7MBVAUDYR3LTN/bundle.json","state_url":"https://pith.science/pith/R32RAQVOQUKPL7MBVAUDYR3LTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R32RAQVOQUKPL7MBVAUDYR3LTN/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":"2026-06-25T22:54:37Z","links":{"resolver":"https://pith.science/pith/R32RAQVOQUKPL7MBVAUDYR3LTN","bundle":"https://pith.science/pith/R32RAQVOQUKPL7MBVAUDYR3LTN/bundle.json","state":"https://pith.science/pith/R32RAQVOQUKPL7MBVAUDYR3LTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R32RAQVOQUKPL7MBVAUDYR3LTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R32RAQVOQUKPL7MBVAUDYR3LTN","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":"8a0a32e9a7a26f9c0c4d0594936f5e6d75891eb68a04b8f8780a56eb88cd2c81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-09T06:27:30Z","title_canon_sha256":"2de6c43b28a1eab11312244908b8e1d8ecd41bdc05c301a9253f67a75ae33d12"},"schema_version":"1.0","source":{"id":"1606.02832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02832","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02832v2","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02832","created_at":"2026-05-18T00:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"R32RAQVOQUKP","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R32RAQVOQUKPL7MB","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R32RAQVO","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:ebd036a9ed8aa54a07133ec8911b77f552cb40724444a8b1f8124d437436bd9f","target":"graph","created_at":"2026-05-18T00:49:24Z","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 work we prove optimal $W^{s,p}$-approximation estimates (with $p\\in[1,+\\infty]$) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont--Scott approximation theory together with two novel abstract lemmas: An approximation result for bounded projectors, and an $L^p$-boundedness result for $L^2$-orthogonal projectors on polynomial subspaces. The $W^{s,p}$-approximation results have general applicability to (standard or polytopal) numerical methods based on local polynomial spaces. As an illustration, we use these $W^{s,p}$-estimates to derive novel e","authors_text":"Daniele Di Pietro, Jerome Droniou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-09T06:27:30Z","title":"$W^{s,p}$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02832","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":"sha256:7378ba7d767a5ae915ca80df82b7f6f537751efabeab2984ea3840e9718f0382","target":"record","created_at":"2026-05-18T00:49:24Z","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":"8a0a32e9a7a26f9c0c4d0594936f5e6d75891eb68a04b8f8780a56eb88cd2c81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-09T06:27:30Z","title_canon_sha256":"2de6c43b28a1eab11312244908b8e1d8ecd41bdc05c301a9253f67a75ae33d12"},"schema_version":"1.0","source":{"id":"1606.02832","kind":"arxiv","version":2}},"canonical_sha256":"8ef51042ae8514f5fd81a8283c476b9b7551bb949cd2fd2ab421f7f7340c60d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ef51042ae8514f5fd81a8283c476b9b7551bb949cd2fd2ab421f7f7340c60d0","first_computed_at":"2026-05-18T00:49:24.594798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:24.594798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0lZemjYHfSWhRl//WyoNg6c0/M9pP3YzfI75XbC1M5WDC598W6ZFa3Nf6pO74RQs3a11AY4lFtVYG+my8A2hBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:24.595498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7378ba7d767a5ae915ca80df82b7f6f537751efabeab2984ea3840e9718f0382","sha256:ebd036a9ed8aa54a07133ec8911b77f552cb40724444a8b1f8124d437436bd9f"],"state_sha256":"1b82409ca277935ff40e3fdb634c5509ff64d8a3395d9b9f51f2757030125d9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1mPnTy6PMQoksSgHILQO2S9Y50B25yaa+aNuFzxykdh3stP+uLYUzprsZymwkaPFIDTruH93gwDOiU9gbOZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:54:37.635924Z","bundle_sha256":"29dce067ecd103e707f7b8abb28eccdcf728731579e745efb5b776040f68d653"}}