{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IEEGIECPFILFOPQJY66LYW74HE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a9804557d343b71232030286dd51ede98e2e8e0f13ca076c55e0ef7dfe3b2d22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-18T15:03:24Z","title_canon_sha256":"296c60d016e4b4520ffbba180e8297149f0c5017dedaa5314a793beb2b2431a3"},"schema_version":"1.0","source":{"id":"1904.09869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09869","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09869v1","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09869","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"IEEGIECPFILF","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IEEGIECPFILFOPQJ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IEEGIECP","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:d5c5c66f323c76bb7cd7ec3af8ef4b14e08df0ab7d2b3e1733d39d17406405d1","target":"graph","created_at":"2026-05-17T23:48:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically accessible. The specific example of application of this work to a time-varying three-dimensional magnetic field is given, but this method would work equally well for a time-independent four-dimensional field. Implementations of both of these methods in the Python programming language are also available to download.","authors_text":"Paul A. Walker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-18T15:03:24Z","title":"Quadcubic interpolation: a four-dimensional spline method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09869","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8cd2c27a7aac3867548557b865f73192a9cca46931ac9af9b46831808adad15e","target":"record","created_at":"2026-05-17T23:48:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a9804557d343b71232030286dd51ede98e2e8e0f13ca076c55e0ef7dfe3b2d22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-18T15:03:24Z","title_canon_sha256":"296c60d016e4b4520ffbba180e8297149f0c5017dedaa5314a793beb2b2431a3"},"schema_version":"1.0","source":{"id":"1904.09869","kind":"arxiv","version":1}},"canonical_sha256":"410864104f2a16573e09c7bcbc5bfc390f463b015d5290da0888f0e854edd0e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"410864104f2a16573e09c7bcbc5bfc390f463b015d5290da0888f0e854edd0e8","first_computed_at":"2026-05-17T23:48:03.015950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:03.015950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lJjCbIvLK1m5Jr1GQIpbT01qri/41O2L6XvforLQ6y+jFsoh4KYTIN2Bw7Bo0t991BAu9Ngr/LEqMda34ZmoBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:03.016505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd2c27a7aac3867548557b865f73192a9cca46931ac9af9b46831808adad15e","sha256:d5c5c66f323c76bb7cd7ec3af8ef4b14e08df0ab7d2b3e1733d39d17406405d1"],"state_sha256":"176621920d97b8ed997bc54970a01b9de606d5a21ad19bdbbf7e304200050b83"}