{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ONBZAHNVFWGEYY2EYU43ZFILQI","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":"9271e4e03921e83867c5a4589a824bfb0ef19ada3d5ebf575ff08ce59ddeacee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-06T22:42:46Z","title_canon_sha256":"a29ecd77eb2e4ce7655a85049740b4d8e898b2745ec9a1e02350832fbe103558"},"schema_version":"1.0","source":{"id":"1411.1786","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1786","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1786v1","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1786","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"ONBZAHNVFWGE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"ONBZAHNVFWGEYY2E","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"ONBZAHNV","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a1440805dbbde9215c712a883eb4871a50f5cc173379d34f806728da6bf02a09","target":"graph","created_at":"2026-05-18T02:38:26Z","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 exhibit an algorithm to solve the following extension problem: Given a finite set $E \\subset \\mathbb{R}^n$ and a function $f: E \\rightarrow \\mathbb{R}$, compute an extension $F$ in the Sobolev space $L^{m,p}(\\mathbb{R}^n)$, $p>n$, with norm having the smallest possible order of magnitude, and secondly, compute the order of magnitude of the norm of $F$. Here, $L^{m,p}(\\mathbb{R}^n)$ denotes the Sobolev space consisting of functions on $\\mathbb{R}^n$ whose $m$th order partial derivatives belong to $L^p(\\mathbb{R}^n)$. The running time of our algorithm is at most $C N \\log N$, where $N$ denote","authors_text":"Arie Israel, Charles L. Fefferman, Garving K. Luli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-06T22:42:46Z","title":"Fitting a Sobolev function to data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1786","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:dfe2af1dea2ba47bc4365ac468efa8922f4236aa127c533e45637463462a234d","target":"record","created_at":"2026-05-18T02:38:26Z","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":"9271e4e03921e83867c5a4589a824bfb0ef19ada3d5ebf575ff08ce59ddeacee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-06T22:42:46Z","title_canon_sha256":"a29ecd77eb2e4ce7655a85049740b4d8e898b2745ec9a1e02350832fbe103558"},"schema_version":"1.0","source":{"id":"1411.1786","kind":"arxiv","version":1}},"canonical_sha256":"7343901db52d8c4c6344c539bc950b821b059175f276cfeefeddff8a86f9943a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7343901db52d8c4c6344c539bc950b821b059175f276cfeefeddff8a86f9943a","first_computed_at":"2026-05-18T02:38:26.006357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:26.006357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"31Gt+nNk3WI6Ameq13fYmZd9HQ2Jd6cbxbDTIXUdD0w4Gx3TB/owxUuiYCOdZTEnknx9JLPqQ4vOmzm/pwC8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:26.006844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1786","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfe2af1dea2ba47bc4365ac468efa8922f4236aa127c533e45637463462a234d","sha256:a1440805dbbde9215c712a883eb4871a50f5cc173379d34f806728da6bf02a09"],"state_sha256":"40fff5ec94a0b19dfde7efd81e59f24964747fb54d7acf4757d51043b8510f41"}