{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:K3YWWC4JN5ZFHXBVB3RSUVC7TA","short_pith_number":"pith:K3YWWC4J","schema_version":"1.0","canonical_sha256":"56f16b0b896f7253dc350ee32a545f981421025e6eda9b74c12f00050cac31bb","source":{"kind":"arxiv","id":"1809.01598","version":2},"attestation_state":"computed","paper":{"title":"Computation of multi-degree B-splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hendrik Speleers","submitted_at":"2018-09-05T16:11:23Z","abstract_excerpt":"Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar properties to standard B-splines. These basis functions are called multi-degree B-splines (or MDB-splines). The construction relies on an extraction operator that represents all MDB-splines as linear combinations of local B-splines of different degrees. This enables the use of existing efficient algorithms for B-spline evaluations and refinements in the context 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":"1809.01598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-05T16:11:23Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fee42a45eb7fc283f164c144620e969f6f5c4c81ee12dd28357fa7f47aa71e0c","abstract_canon_sha256":"97372ec13a33ed26169c17380c49b862d033401dcabafa2cf494c72ecbf67b1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:17.922238Z","signature_b64":"HNNNhA+8LWlJekSrCsZCjWnK3NNjtvAjoozoe0C/5Obp2brWEgpvqVCpAP5z/m7R+Ct5Del5PN1hfMlhyR9iCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56f16b0b896f7253dc350ee32a545f981421025e6eda9b74c12f00050cac31bb","last_reissued_at":"2026-06-04T20:13:17.921763Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:17.921763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computation of multi-degree B-splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hendrik Speleers","submitted_at":"2018-09-05T16:11:23Z","abstract_excerpt":"Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar properties to standard B-splines. These basis functions are called multi-degree B-splines (or MDB-splines). The construction relies on an extraction operator that represents all MDB-splines as linear combinations of local B-splines of different degrees. This enables the use of existing efficient algorithms for B-spline evaluations and refinements in the context of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01598","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1809.01598/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":"1809.01598","created_at":"2026-06-04T20:13:17.921822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01598v2","created_at":"2026-06-04T20:13:17.921822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01598","created_at":"2026-06-04T20:13:17.921822+00:00"},{"alias_kind":"pith_short_12","alias_value":"K3YWWC4JN5ZF","created_at":"2026-06-04T20:13:17.921822+00:00"},{"alias_kind":"pith_short_16","alias_value":"K3YWWC4JN5ZFHXBV","created_at":"2026-06-04T20:13:17.921822+00:00"},{"alias_kind":"pith_short_8","alias_value":"K3YWWC4J","created_at":"2026-06-04T20:13:17.921822+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/K3YWWC4JN5ZFHXBVB3RSUVC7TA","json":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA.json","graph_json":"https://pith.science/api/pith-number/K3YWWC4JN5ZFHXBVB3RSUVC7TA/graph.json","events_json":"https://pith.science/api/pith-number/K3YWWC4JN5ZFHXBVB3RSUVC7TA/events.json","paper":"https://pith.science/paper/K3YWWC4J"},"agent_actions":{"view_html":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA","download_json":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA.json","view_paper":"https://pith.science/paper/K3YWWC4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01598&json=true","fetch_graph":"https://pith.science/api/pith-number/K3YWWC4JN5ZFHXBVB3RSUVC7TA/graph.json","fetch_events":"https://pith.science/api/pith-number/K3YWWC4JN5ZFHXBVB3RSUVC7TA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA/action/storage_attestation","attest_author":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA/action/author_attestation","sign_citation":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA/action/citation_signature","submit_replication":"https://pith.science/pith/K3YWWC4JN5ZFHXBVB3RSUVC7TA/action/replication_record"}},"created_at":"2026-06-04T20:13:17.921822+00:00","updated_at":"2026-06-04T20:13:17.921822+00:00"}