{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4H5S5PHU6SOTGQUVXWCW2TSLHD","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":"7f297b6dcc8b3dd66322400a5bbb3bbfadac1a02cc03061f230f9ef3faea5d08","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-11-06T08:13:15Z","title_canon_sha256":"a8d2c8d8f0e31f321948b1fcc72a30cd00fcbcdad8197278cbc60b3179cbb8a5"},"schema_version":"1.0","source":{"id":"1411.1519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1519","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1519v1","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1519","created_at":"2026-05-18T02:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"4H5S5PHU6SOT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4H5S5PHU6SOTGQUV","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4H5S5PHU","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:2c6ad0a1030e662801ec1665cfc15a9636e6b71d53c6e254aa8486fddb2d10ac","target":"graph","created_at":"2026-05-18T02:38:27Z","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":"Let $k$ be a nonnegative integer. In the approximate $k$-flat nearest neighbor ($k$-ANN) problem, we are given a set $P \\subset \\mathbb{R}^d$ of $n$ points in $d$-dimensional space and a fixed approximation factor $c > 1$. Our goal is to preprocess $P$ so that we can efficiently answer approximate $k$-flat nearest neighbor queries: given a $k$-flat $F$, find a point in $P$ whose distance to $F$ is within a factor $c$ of the distance between $F$ and the closest point in $P$. The case $k = 0$ corresponds to the well-studied approximate nearest neighbor problem, for which a plethora of results ar","authors_text":"Huy L. Nguyen, Paul Seiferth, Wolfgang Mulzer, Yannik Stein","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-11-06T08:13:15Z","title":"Approximate k-flat Nearest Neighbor Search"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1519","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":"sha256:8da11324c13bdea4e6b6605f235dc3147288262c2fd47e5528d6324abbf3d756","target":"record","created_at":"2026-05-18T02:38:27Z","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":"7f297b6dcc8b3dd66322400a5bbb3bbfadac1a02cc03061f230f9ef3faea5d08","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-11-06T08:13:15Z","title_canon_sha256":"a8d2c8d8f0e31f321948b1fcc72a30cd00fcbcdad8197278cbc60b3179cbb8a5"},"schema_version":"1.0","source":{"id":"1411.1519","kind":"arxiv","version":1}},"canonical_sha256":"e1fb2ebcf4f49d334295bd856d4e4b38f43e3ac32351f6c7a47fa1845f979b3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1fb2ebcf4f49d334295bd856d4e4b38f43e3ac32351f6c7a47fa1845f979b3b","first_computed_at":"2026-05-18T02:38:27.709221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:27.709221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"knbueoOHM7F9Uj+oLmzPouMQ3nffo93ap0Xs+34eyu0a+jFWnV4I5rgwHNsLdaNBuOpegkLxuLakNkl9vgnTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:27.709732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da11324c13bdea4e6b6605f235dc3147288262c2fd47e5528d6324abbf3d756","sha256:2c6ad0a1030e662801ec1665cfc15a9636e6b71d53c6e254aa8486fddb2d10ac"],"state_sha256":"74f4538440d31f3c7142387b08c388f7676abfdd9eb8c9b6cd442b8fd0e9a8c1"}