{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TKJTM65O5DNRAIRNK4HK57VQTW","short_pith_number":"pith:TKJTM65O","schema_version":"1.0","canonical_sha256":"9a93367baee8db10222d570eaefeb09da6c45b3d904a38d5faa66658b17b5dbb","source":{"kind":"arxiv","id":"2505.14909","version":4},"attestation_state":"computed","paper":{"title":"Accelerating Multivariate Newton Interpolation in Downward Closed Polynomial Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Michael Hecht, Phil-Alexander Hofmann","submitted_at":"2025-05-20T21:03:33Z","abstract_excerpt":"We introduce the fast Newton transform (FNT), a multivariate Newton interpolation algorithm for downward closed polynomial spaces in quasi-tensorial grids. The FNT computes the Newton coefficients directly, without relying on embeddings into enclosing tensor-product spaces. For a downward closed index set $A \\subset \\mathbb N_0^m$, the FNT achieves a time complexity of $\\mathcal O(m \\overline n |A|)$, where $\\overline n$ is the mean of the coordinate-wise maximal polynomial degrees $n_1, \\ldots, n_m$ across the $m$ spatial dimensions. In the univariate case, the FNT renders the classic Newton "},"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":"2505.14909","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-20T21:03:33Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0e6a1ef5f1a53f4500e7c9d9389f8333af1b4075a2b26bab1e8f8e9091a22c4e","abstract_canon_sha256":"06e3021158e0df43ca5ef04d5855c9a98ecd1d0420a21f8f26b32603b0f7297d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:45.508496Z","signature_b64":"/SBQm9gSKFA40s5CCf1U/2B5JYffvajDwj/ShrsU3neG0YvGwucsufFOTqZ1BbN+Gd7Y7OC78pkqCrrguf03Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a93367baee8db10222d570eaefeb09da6c45b3d904a38d5faa66658b17b5dbb","last_reissued_at":"2026-06-23T03:13:45.507991Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:45.507991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Accelerating Multivariate Newton Interpolation in Downward Closed Polynomial Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Michael Hecht, Phil-Alexander Hofmann","submitted_at":"2025-05-20T21:03:33Z","abstract_excerpt":"We introduce the fast Newton transform (FNT), a multivariate Newton interpolation algorithm for downward closed polynomial spaces in quasi-tensorial grids. The FNT computes the Newton coefficients directly, without relying on embeddings into enclosing tensor-product spaces. For a downward closed index set $A \\subset \\mathbb N_0^m$, the FNT achieves a time complexity of $\\mathcal O(m \\overline n |A|)$, where $\\overline n$ is the mean of the coordinate-wise maximal polynomial degrees $n_1, \\ldots, n_m$ across the $m$ spatial dimensions. In the univariate case, the FNT renders the classic Newton "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14909","kind":"arxiv","version":4},"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/2505.14909/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":"2505.14909","created_at":"2026-06-23T03:13:45.508058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.14909v4","created_at":"2026-06-23T03:13:45.508058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14909","created_at":"2026-06-23T03:13:45.508058+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKJTM65O5DNR","created_at":"2026-06-23T03:13:45.508058+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKJTM65O5DNRAIRN","created_at":"2026-06-23T03:13:45.508058+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKJTM65O","created_at":"2026-06-23T03:13:45.508058+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/TKJTM65O5DNRAIRNK4HK57VQTW","json":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW.json","graph_json":"https://pith.science/api/pith-number/TKJTM65O5DNRAIRNK4HK57VQTW/graph.json","events_json":"https://pith.science/api/pith-number/TKJTM65O5DNRAIRNK4HK57VQTW/events.json","paper":"https://pith.science/paper/TKJTM65O"},"agent_actions":{"view_html":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW","download_json":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW.json","view_paper":"https://pith.science/paper/TKJTM65O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.14909&json=true","fetch_graph":"https://pith.science/api/pith-number/TKJTM65O5DNRAIRNK4HK57VQTW/graph.json","fetch_events":"https://pith.science/api/pith-number/TKJTM65O5DNRAIRNK4HK57VQTW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW/action/storage_attestation","attest_author":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW/action/author_attestation","sign_citation":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW/action/citation_signature","submit_replication":"https://pith.science/pith/TKJTM65O5DNRAIRNK4HK57VQTW/action/replication_record"}},"created_at":"2026-06-23T03:13:45.508058+00:00","updated_at":"2026-06-23T03:13:45.508058+00:00"}