{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QI4STXSAST3XYQTZ3AODPYXREX","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":"3dd4274d111c026234134c2de8f7460f05630275e7bbb6ba14e723e82b8cfd7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-09-20T19:18:08Z","title_canon_sha256":"a55ad59f6d837064de040d60e0b1aa0106c010eda152de917075cca20e783c6b"},"schema_version":"1.0","source":{"id":"1609.06295","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06295","created_at":"2026-05-18T00:56:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06295v3","created_at":"2026-05-18T00:56:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06295","created_at":"2026-05-18T00:56:19Z"},{"alias_kind":"pith_short_12","alias_value":"QI4STXSAST3X","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QI4STXSAST3XYQTZ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QI4STXSA","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:682369747a5e4cf12779094d4bda0404721063582471b2d110ed3e3885c615d0","target":"graph","created_at":"2026-05-18T00:56:19Z","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":"The metric sketching problem is defined as follows. Given a metric on $n$ points, and $\\epsilon>0$, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up to a $1+\\epsilon$ distortion. In this paper we consider metrics induced by $\\ell_2$ and $\\ell_1$ norms whose spread (the ratio of the diameter to the closest pair distance) is bounded by $\\Phi>0$. A well-known dimensionality reduction theorem due to Johnson and Lindenstrauss yields a sketch of size $O(\\epsilon^{-2} \\log (\\Phi n) n\\log n)$, i.e., $O(\\epsilon^{","authors_text":"Piotr Indyk, Tal Wagner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-09-20T19:18:08Z","title":"Near-Optimal (Euclidean) Metric Compression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06295","kind":"arxiv","version":3},"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":"sha256:50e1373acca62967a8470767ad128b336122d68600877d03371a09543ab4ed8e","target":"record","created_at":"2026-05-18T00:56:19Z","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":"3dd4274d111c026234134c2de8f7460f05630275e7bbb6ba14e723e82b8cfd7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-09-20T19:18:08Z","title_canon_sha256":"a55ad59f6d837064de040d60e0b1aa0106c010eda152de917075cca20e783c6b"},"schema_version":"1.0","source":{"id":"1609.06295","kind":"arxiv","version":3}},"canonical_sha256":"823929de4094f77c4279d81c37e2f125c802c5ee7e8397630403df3c28b5acc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823929de4094f77c4279d81c37e2f125c802c5ee7e8397630403df3c28b5acc5","first_computed_at":"2026-05-18T00:56:19.420147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:19.420147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVUgUfs+EP/TpSKK9J+4rnhKaT2KwGzjFAm9lAgXulCIzKqsPR5hsaHRbkAMRVRcNgGRsZgh0013RoMdpcNpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:19.420915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06295","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50e1373acca62967a8470767ad128b336122d68600877d03371a09543ab4ed8e","sha256:682369747a5e4cf12779094d4bda0404721063582471b2d110ed3e3885c615d0"],"state_sha256":"d227bea85f313eee5fe15ef68e71403b73e166af9118bec04419f1fd1b0f6038"}