{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HQWXQRWLJG3IXURFNAQB2I4Q7L","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":"3cb172d000504de967b431c3ce92666565c16e169a74cb442b3a99bfa5bd4a38","cross_cats_sorted":["cs.DS","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-05-01T22:30:45Z","title_canon_sha256":"27b90dadf051659e2fb1453105469872e8d3680f27a4dba48407cbcc2b18165c"},"schema_version":"1.0","source":{"id":"1505.00290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00290","created_at":"2026-05-18T01:37:34Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00290v2","created_at":"2026-05-18T01:37:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00290","created_at":"2026-05-18T01:37:34Z"},{"alias_kind":"pith_short_12","alias_value":"HQWXQRWLJG3I","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HQWXQRWLJG3IXURF","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HQWXQRWL","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:5d97e66be963c6e679d1bc7c6ed443557e352b6d829465d1cd0b880b44f7ec47","target":"graph","created_at":"2026-05-18T01:37:34Z","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 develop fast algorithms for solving regression problems on graphs where one is given the value of a function at some vertices, and must find its smoothest possible extension to all vertices. The extension we compute is the absolutely minimal Lipschitz extension, and is the limit for large $p$ of $p$-Laplacian regularization. We present an algorithm that computes a minimal Lipschitz extension in expected linear time, and an algorithm that computes an absolutely minimal Lipschitz extension in expected time $\\widetilde{O} (m n)$. The latter algorithm has variants that seem to run much faster i","authors_text":"Anup Rao, Daniel A. Spielman, Rasmus Kyng, Sushant Sachdeva","cross_cats":["cs.DS","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-05-01T22:30:45Z","title":"Algorithms for Lipschitz Learning on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00290","kind":"arxiv","version":2},"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":"sha256:70aa927d5daeef03023ac132e89a02c1356a44413a0e308f10b3039aa25eb105","target":"record","created_at":"2026-05-18T01:37:34Z","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":"3cb172d000504de967b431c3ce92666565c16e169a74cb442b3a99bfa5bd4a38","cross_cats_sorted":["cs.DS","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-05-01T22:30:45Z","title_canon_sha256":"27b90dadf051659e2fb1453105469872e8d3680f27a4dba48407cbcc2b18165c"},"schema_version":"1.0","source":{"id":"1505.00290","kind":"arxiv","version":2}},"canonical_sha256":"3c2d7846cb49b68bd22568201d2390fac50b02e2eb22712826f1b35ad35508bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c2d7846cb49b68bd22568201d2390fac50b02e2eb22712826f1b35ad35508bf","first_computed_at":"2026-05-18T01:37:34.655130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:34.655130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MC5J2yZYfbDeW97RaIaEQdJ+Jt4pMnRijTLmK3xJMCdncMfKa0+QHLmd0m6fPwrg43WU64o9rg4Ye4tm8loeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:34.655667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70aa927d5daeef03023ac132e89a02c1356a44413a0e308f10b3039aa25eb105","sha256:5d97e66be963c6e679d1bc7c6ed443557e352b6d829465d1cd0b880b44f7ec47"],"state_sha256":"314482adf2889541619b5ced33fa5ff185265a627d8ccfd7fd46e89914cacfea"}