{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:N2PRTE2UOY5E66KNEOBSAR3YFG","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":"b3c1b37475f87d94ef7e5f3f9ac015bb5375110491b152da0f79fb3c67774ee0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-04-24T19:20:31Z","title_canon_sha256":"226bda5c853c7fd27982d2287018a1be9741420b7ef59d70e79a6a9953597103"},"schema_version":"1.0","source":{"id":"2504.17899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.17899","created_at":"2026-07-05T10:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"2504.17899v1","created_at":"2026-07-05T10:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.17899","created_at":"2026-07-05T10:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"N2PRTE2UOY5E","created_at":"2026-07-05T10:53:58Z"},{"alias_kind":"pith_short_16","alias_value":"N2PRTE2UOY5E66KN","created_at":"2026-07-05T10:53:58Z"},{"alias_kind":"pith_short_8","alias_value":"N2PRTE2U","created_at":"2026-07-05T10:53:58Z"}],"graph_snapshots":[{"event_id":"sha256:68a6e28e32de25e859940d2638b07a12eaed4bb8fd5e0bc4a3f292eb38d7d71a","target":"graph","created_at":"2026-07-05T10:53:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.17899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runtime and linear storage cost. The generalisation supports any choice of the provided notion of non-tensorial unisolvent interpolation nodes, whose number coincides with the dimension of the chosen-downward closed space. Specifically, we prove that by selecting Leja-ordered Chebyshev-Lobatto or Leja nodes, the optimal geometric approximation rates for a class of analytic functions -- termed Bos--Levenberg--Trefethen fun","authors_text":"Damar Wicaksono, Ivo F. Sbalzarini, Jannik Kissinger, Krzysztof Gonciarz, Michael Hecht, Phil-Alexander Hofmann, Uwe Hernandez Acosta, Vladimir Sivkin","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-04-24T19:20:31Z","title":"Multivariate Newton Interpolation in Downward Closed Spaces Reaches the Optimal Geometric Approximation Rates for Bos--Levenberg--Trefethen Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17899","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":"sha256:33f8e5a1af9efbeab6e8cb7b2ee16bf891e64587f83ace505d4151ec47c10bcc","target":"record","created_at":"2026-07-05T10:53:58Z","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":"b3c1b37475f87d94ef7e5f3f9ac015bb5375110491b152da0f79fb3c67774ee0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-04-24T19:20:31Z","title_canon_sha256":"226bda5c853c7fd27982d2287018a1be9741420b7ef59d70e79a6a9953597103"},"schema_version":"1.0","source":{"id":"2504.17899","kind":"arxiv","version":1}},"canonical_sha256":"6e9f199354763a4f794d2383204778299486974c6312beef5873aee1f2e8bc9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e9f199354763a4f794d2383204778299486974c6312beef5873aee1f2e8bc9f","first_computed_at":"2026-07-05T10:53:58.381491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:53:58.381491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jbxFQiXNWXRyBUS7bb+9e60B8MMpNu2Sm1K/0ssBaLwNR7NdcwLXfjuS2C7cGVFZD9u3BiO2VxvoABbgfkQcAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:53:58.382037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.17899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f8e5a1af9efbeab6e8cb7b2ee16bf891e64587f83ace505d4151ec47c10bcc","sha256:68a6e28e32de25e859940d2638b07a12eaed4bb8fd5e0bc4a3f292eb38d7d71a"],"state_sha256":"279784c8b9e87915de81e7a165435ba1b6630ebf3c5ca0a9ec8428cd267047ef"}