{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:F4RWXCCDWT7TLFN7C6S236S4BJ","short_pith_number":"pith:F4RWXCCD","schema_version":"1.0","canonical_sha256":"2f236b8843b4ff3595bf17a5adfa5c0a6750bdaf59ed8d9b3c11366342030b5f","source":{"kind":"arxiv","id":"1908.06199","version":1},"attestation_state":"computed","paper":{"title":"Quadrature rules for $C^0$ and $C^1$ splines, a recipe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Helmut Ruhland","submitted_at":"2019-08-16T22:48:21Z","abstract_excerpt":"Closed formulae for all Gaussian or optimal, 1-parameter quadrature rules in a compact interval [a, b] with non uniform, asymmetric subintervals, arbitrary number of nodes per subinterval for the spline classes $S_{2N, 0}$ and $S_{2N+1, 1}$, i.e. even and odd degree are presented. Also rules for the 2 missing spline classes $S_{2N-1, 0}$ and $S_{2N, 1}$ (the so called 1/2-rules), i.e. odd and even degree are presented. These quadrature rules are explicit in the sense, that they compute the nodes and their weights in the first/last boundary subinterval and, via a recursion the other nodes/weigh"},"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":"1908.06199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-16T22:48:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d82b950d5ae75ac5cea19be735ee8fae293a24d5aeeddecc1621a4d6ebc52ca9","abstract_canon_sha256":"86bb29cbd180134c9d1ae4ecd1e093668dacc83b678919a9a7257f6a68cbdb08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:13.435639Z","signature_b64":"+CSIajR77ZpKL3v1dVtk9J8DcbUyYleGZP2nwP7yCQIbwnbYJpZes7qdHcd8qeZNtIl/HfeP6txmy8ff27ncDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f236b8843b4ff3595bf17a5adfa5c0a6750bdaf59ed8d9b3c11366342030b5f","last_reissued_at":"2026-07-04T23:58:13.435171Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:13.435171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadrature rules for $C^0$ and $C^1$ splines, a recipe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Helmut Ruhland","submitted_at":"2019-08-16T22:48:21Z","abstract_excerpt":"Closed formulae for all Gaussian or optimal, 1-parameter quadrature rules in a compact interval [a, b] with non uniform, asymmetric subintervals, arbitrary number of nodes per subinterval for the spline classes $S_{2N, 0}$ and $S_{2N+1, 1}$, i.e. even and odd degree are presented. Also rules for the 2 missing spline classes $S_{2N-1, 0}$ and $S_{2N, 1}$ (the so called 1/2-rules), i.e. odd and even degree are presented. These quadrature rules are explicit in the sense, that they compute the nodes and their weights in the first/last boundary subinterval and, via a recursion the other nodes/weigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06199","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/1908.06199/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":"1908.06199","created_at":"2026-07-04T23:58:13.435230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06199v1","created_at":"2026-07-04T23:58:13.435230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06199","created_at":"2026-07-04T23:58:13.435230+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4RWXCCDWT7T","created_at":"2026-07-04T23:58:13.435230+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4RWXCCDWT7TLFN7","created_at":"2026-07-04T23:58:13.435230+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4RWXCCD","created_at":"2026-07-04T23:58:13.435230+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/F4RWXCCDWT7TLFN7C6S236S4BJ","json":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ.json","graph_json":"https://pith.science/api/pith-number/F4RWXCCDWT7TLFN7C6S236S4BJ/graph.json","events_json":"https://pith.science/api/pith-number/F4RWXCCDWT7TLFN7C6S236S4BJ/events.json","paper":"https://pith.science/paper/F4RWXCCD"},"agent_actions":{"view_html":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ","download_json":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ.json","view_paper":"https://pith.science/paper/F4RWXCCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06199&json=true","fetch_graph":"https://pith.science/api/pith-number/F4RWXCCDWT7TLFN7C6S236S4BJ/graph.json","fetch_events":"https://pith.science/api/pith-number/F4RWXCCDWT7TLFN7C6S236S4BJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ/action/storage_attestation","attest_author":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ/action/author_attestation","sign_citation":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ/action/citation_signature","submit_replication":"https://pith.science/pith/F4RWXCCDWT7TLFN7C6S236S4BJ/action/replication_record"}},"created_at":"2026-07-04T23:58:13.435230+00:00","updated_at":"2026-07-04T23:58:13.435230+00:00"}