{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2OBQAYIQ54VEELE6IRXELLSFPO","short_pith_number":"pith:2OBQAYIQ","schema_version":"1.0","canonical_sha256":"d383006110ef2a422c9e446e45ae457b92600f00f1b13ae063c2ce3252ebcdeb","source":{"kind":"arxiv","id":"1505.05392","version":3},"attestation_state":"computed","paper":{"title":"Globally structured 3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Philipp Morgenstern","submitted_at":"2015-05-20T14:15:21Z","abstract_excerpt":"This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to dual-compatibility, wich guarantees linear independence of the T-spline blending functions. In addition, we present a local refinement algorithm that generates analysis-suitable meshes and has linear computational complexity in terms of the number of marked and generated mesh elements."},"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":"1505.05392","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-20T14:15:21Z","cross_cats_sorted":[],"title_canon_sha256":"63b3626704548d1e03ca0b516625950f7e390537132cd0760810bca8de6322e1","abstract_canon_sha256":"6b626229b44644e585a60322eac341d9c7acd46e0ce2a3a2f4cc4200ed4f37cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:23.992779Z","signature_b64":"bpR5BcoeGCgnbZ8GHiJHHU7X4rm3R41nnqKb3mqOT8Lc+p63luMis0sD1BoK0V3WqRUCUVZ1gND/ciDkzD0PBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d383006110ef2a422c9e446e45ae457b92600f00f1b13ae063c2ce3252ebcdeb","last_reissued_at":"2026-05-18T00:52:23.992166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:23.992166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Globally structured 3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Philipp Morgenstern","submitted_at":"2015-05-20T14:15:21Z","abstract_excerpt":"This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to dual-compatibility, wich guarantees linear independence of the T-spline blending functions. In addition, we present a local refinement algorithm that generates analysis-suitable meshes and has linear computational complexity in terms of the number of marked and generated mesh elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05392","kind":"arxiv","version":3},"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":"1505.05392","created_at":"2026-05-18T00:52:23.992263+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.05392v3","created_at":"2026-05-18T00:52:23.992263+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05392","created_at":"2026-05-18T00:52:23.992263+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OBQAYIQ54VE","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OBQAYIQ54VEELE6","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OBQAYIQ","created_at":"2026-05-18T12:29:02.477457+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/2OBQAYIQ54VEELE6IRXELLSFPO","json":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO.json","graph_json":"https://pith.science/api/pith-number/2OBQAYIQ54VEELE6IRXELLSFPO/graph.json","events_json":"https://pith.science/api/pith-number/2OBQAYIQ54VEELE6IRXELLSFPO/events.json","paper":"https://pith.science/paper/2OBQAYIQ"},"agent_actions":{"view_html":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO","download_json":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO.json","view_paper":"https://pith.science/paper/2OBQAYIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.05392&json=true","fetch_graph":"https://pith.science/api/pith-number/2OBQAYIQ54VEELE6IRXELLSFPO/graph.json","fetch_events":"https://pith.science/api/pith-number/2OBQAYIQ54VEELE6IRXELLSFPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO/action/storage_attestation","attest_author":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO/action/author_attestation","sign_citation":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO/action/citation_signature","submit_replication":"https://pith.science/pith/2OBQAYIQ54VEELE6IRXELLSFPO/action/replication_record"}},"created_at":"2026-05-18T00:52:23.992263+00:00","updated_at":"2026-05-18T00:52:23.992263+00:00"}