{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OEVZJK7XVTPXZBPALTICMIS4BN","short_pith_number":"pith:OEVZJK7X","schema_version":"1.0","canonical_sha256":"712b94abf7acdf7c85e05cd026225c0b62a30503a6dbc44b7ad991ded8951dc1","source":{"kind":"arxiv","id":"1709.00577","version":1},"attestation_state":"computed","paper":{"title":"Constants in Discrete Poincar\\'e and Friedrichs Inequalities and Discrete Quasi-Interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carsten Carstensen, Friederike Hellwig","submitted_at":"2017-09-02T13:27:57Z","abstract_excerpt":"This paper provides a discrete Poincar\\'e inequality in $n$ space dimensions on a simplex $K$ with explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero on $K$ and all integrals of jumps zero along all interior sides by its Lebesgue norm by $C(n)\\operatorname{diam}(K)$. The explicit constant $C(n)$ depends only on the dimension $n=2,3$ in case of an adaptive triangulation with the newest vertex bisection. The second part of this paper proves the stability of an enrichment operator, which leads to the stability and approximation of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.00577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-02T13:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"0be8669ff07b529571301e4eaaae07fd028b7ceb1948b22a80bd59cf22bf0217","abstract_canon_sha256":"3b361eab554cfeb22c106cdd1253fa4e130ece7c7db9637e307b42cc0c338530"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:07.616734Z","signature_b64":"Qv1QOIk5fVwslf29YAopaX0gPhV1uG2Tj6IM1lFDJMSqyGkPT8xs96UP4EsYLQsxexcnUCfAd5ReZBr/BckbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"712b94abf7acdf7c85e05cd026225c0b62a30503a6dbc44b7ad991ded8951dc1","last_reissued_at":"2026-05-18T00:36:07.616030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:07.616030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constants in Discrete Poincar\\'e and Friedrichs Inequalities and Discrete Quasi-Interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carsten Carstensen, Friederike Hellwig","submitted_at":"2017-09-02T13:27:57Z","abstract_excerpt":"This paper provides a discrete Poincar\\'e inequality in $n$ space dimensions on a simplex $K$ with explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero on $K$ and all integrals of jumps zero along all interior sides by its Lebesgue norm by $C(n)\\operatorname{diam}(K)$. The explicit constant $C(n)$ depends only on the dimension $n=2,3$ in case of an adaptive triangulation with the newest vertex bisection. The second part of this paper proves the stability of an enrichment operator, which leads to the stability and approximation of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00577","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.00577","created_at":"2026-05-18T00:36:07.616147+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.00577v1","created_at":"2026-05-18T00:36:07.616147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00577","created_at":"2026-05-18T00:36:07.616147+00:00"},{"alias_kind":"pith_short_12","alias_value":"OEVZJK7XVTPX","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OEVZJK7XVTPXZBPA","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OEVZJK7X","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN","json":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN.json","graph_json":"https://pith.science/api/pith-number/OEVZJK7XVTPXZBPALTICMIS4BN/graph.json","events_json":"https://pith.science/api/pith-number/OEVZJK7XVTPXZBPALTICMIS4BN/events.json","paper":"https://pith.science/paper/OEVZJK7X"},"agent_actions":{"view_html":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN","download_json":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN.json","view_paper":"https://pith.science/paper/OEVZJK7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.00577&json=true","fetch_graph":"https://pith.science/api/pith-number/OEVZJK7XVTPXZBPALTICMIS4BN/graph.json","fetch_events":"https://pith.science/api/pith-number/OEVZJK7XVTPXZBPALTICMIS4BN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN/action/storage_attestation","attest_author":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN/action/author_attestation","sign_citation":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN/action/citation_signature","submit_replication":"https://pith.science/pith/OEVZJK7XVTPXZBPALTICMIS4BN/action/replication_record"}},"created_at":"2026-05-18T00:36:07.616147+00:00","updated_at":"2026-05-18T00:36:07.616147+00:00"}