{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:I6GEYYO5MSCC77XIYQ7X7VGVIS","short_pith_number":"pith:I6GEYYO5","schema_version":"1.0","canonical_sha256":"478c4c61dd64842ffee8c43f7fd4d544b7d310d6587d38bb338c1b8b560e6c1b","source":{"kind":"arxiv","id":"2003.12097","version":1},"attestation_state":"computed","paper":{"title":"Tuned Hybrid Non-Uniform Subdivision Surfaces with Optimal Convergence Rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Thomas J. R. Hughes, Xiaodong Wei, Xin Li, Yongjie Jessica Zhang","submitted_at":"2020-03-26T18:30:56Z","abstract_excerpt":"This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter $\\lambda$ ($\\frac{1}{4}<\\lambda<1$) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid non-uniform subdivision (tHNUS). Our previous work corresponds to the case when $\\lambda=\\frac{1}{2}$. While introducing $\\lambda$ in hybrid subdivision significantly complicates the theoretical proof of $G^1$ continuity around extraordinary vertices, reducing $\\lambda$ can r"},"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":"2003.12097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-03-26T18:30:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f070123a8668303912c4cf8f99c5d147958d2a9c4d3281fbaeb97aa3122e0284","abstract_canon_sha256":"313151da380ff86b111b0160ed9860d8392ad777e44fb8fa871d2096956626c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:50:55.440794Z","signature_b64":"GwBjxADoGJwVBYLT1UJsWd2KH2k5BbW6ECw9524OBqHdEXoN4yeEr/vBvcJCSbPeMh+GVf+C2Eioa6mGVD91Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"478c4c61dd64842ffee8c43f7fd4d544b7d310d6587d38bb338c1b8b560e6c1b","last_reissued_at":"2026-07-05T00:50:55.440367Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:50:55.440367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tuned Hybrid Non-Uniform Subdivision Surfaces with Optimal Convergence Rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Thomas J. R. Hughes, Xiaodong Wei, Xin Li, Yongjie Jessica Zhang","submitted_at":"2020-03-26T18:30:56Z","abstract_excerpt":"This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter $\\lambda$ ($\\frac{1}{4}<\\lambda<1$) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid non-uniform subdivision (tHNUS). Our previous work corresponds to the case when $\\lambda=\\frac{1}{2}$. While introducing $\\lambda$ in hybrid subdivision significantly complicates the theoretical proof of $G^1$ continuity around extraordinary vertices, reducing $\\lambda$ can r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.12097","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.12097/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2003.12097","created_at":"2026-07-05T00:50:55.440434+00:00"},{"alias_kind":"arxiv_version","alias_value":"2003.12097v1","created_at":"2026-07-05T00:50:55.440434+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.12097","created_at":"2026-07-05T00:50:55.440434+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6GEYYO5MSCC","created_at":"2026-07-05T00:50:55.440434+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6GEYYO5MSCC77XI","created_at":"2026-07-05T00:50:55.440434+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6GEYYO5","created_at":"2026-07-05T00:50:55.440434+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/I6GEYYO5MSCC77XIYQ7X7VGVIS","json":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS.json","graph_json":"https://pith.science/api/pith-number/I6GEYYO5MSCC77XIYQ7X7VGVIS/graph.json","events_json":"https://pith.science/api/pith-number/I6GEYYO5MSCC77XIYQ7X7VGVIS/events.json","paper":"https://pith.science/paper/I6GEYYO5"},"agent_actions":{"view_html":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS","download_json":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS.json","view_paper":"https://pith.science/paper/I6GEYYO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2003.12097&json=true","fetch_graph":"https://pith.science/api/pith-number/I6GEYYO5MSCC77XIYQ7X7VGVIS/graph.json","fetch_events":"https://pith.science/api/pith-number/I6GEYYO5MSCC77XIYQ7X7VGVIS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS/action/storage_attestation","attest_author":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS/action/author_attestation","sign_citation":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS/action/citation_signature","submit_replication":"https://pith.science/pith/I6GEYYO5MSCC77XIYQ7X7VGVIS/action/replication_record"}},"created_at":"2026-07-05T00:50:55.440434+00:00","updated_at":"2026-07-05T00:50:55.440434+00:00"}