{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:EXDOWNAVXKC2JLU3IAZ6IWDORH","short_pith_number":"pith:EXDOWNAV","schema_version":"1.0","canonical_sha256":"25c6eb3415ba85a4ae9b4033e4586e89d39d531a34c923a286b55a4b37514d17","source":{"kind":"arxiv","id":"2306.11604","version":4},"attestation_state":"computed","paper":{"title":"Composition of nested embeddings with an application to outlier removal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kristin Sheridan, Shuchi Chawla","submitted_at":"2023-06-20T15:31:14Z","abstract_excerpt":"We study the design of embeddings into Euclidean space with outliers. Given a metric space $(X,d)$ and an integer $k$, the goal is to embed all but $k$ points in $X$ (called the ``outliers\") into $\\ell_2$ with the smallest possible distortion $c$. Finding the optimal distortion $c$ for a given outlier set size $k$, or alternately the smallest $k$ for a given target distortion $c$ are both NP-hard problems. In fact, it is UGC-hard to approximate $k$ to within a factor smaller than $2$ even when the metric sans outliers is isometrically embeddable into $\\ell_2$. We consider bi-criteria approxima"},"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":"2306.11604","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-06-20T15:31:14Z","cross_cats_sorted":[],"title_canon_sha256":"face2bbedc31a7e27367910b2fea6269981aec36edd5d77154305fb193dda556","abstract_canon_sha256":"20219225fc3f1dbeefc2f675a7bdf1815fcbd1a67c338c97a70493402c794d31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:09:49.835170Z","signature_b64":"o047pxmmWR0M+ZaZu5dG5Gz4cH3Zx5n4C/K5guzWMDd2J9AvzyKpdEd6wHcnepwEFJBPygtZ3bSZ52QepBPZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c6eb3415ba85a4ae9b4033e4586e89d39d531a34c923a286b55a4b37514d17","last_reissued_at":"2026-07-05T07:09:49.834627Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:09:49.834627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Composition of nested embeddings with an application to outlier removal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kristin Sheridan, Shuchi Chawla","submitted_at":"2023-06-20T15:31:14Z","abstract_excerpt":"We study the design of embeddings into Euclidean space with outliers. Given a metric space $(X,d)$ and an integer $k$, the goal is to embed all but $k$ points in $X$ (called the ``outliers\") into $\\ell_2$ with the smallest possible distortion $c$. Finding the optimal distortion $c$ for a given outlier set size $k$, or alternately the smallest $k$ for a given target distortion $c$ are both NP-hard problems. In fact, it is UGC-hard to approximate $k$ to within a factor smaller than $2$ even when the metric sans outliers is isometrically embeddable into $\\ell_2$. We consider bi-criteria approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11604","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/2306.11604/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":"2306.11604","created_at":"2026-07-05T07:09:49.834710+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.11604v4","created_at":"2026-07-05T07:09:49.834710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.11604","created_at":"2026-07-05T07:09:49.834710+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXDOWNAVXKC2","created_at":"2026-07-05T07:09:49.834710+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXDOWNAVXKC2JLU3","created_at":"2026-07-05T07:09:49.834710+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXDOWNAV","created_at":"2026-07-05T07:09:49.834710+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.13784","citing_title":"ScholarSearch: Benchmarking Scholar Searching Ability of LLMs","ref_index":2023,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH","json":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH.json","graph_json":"https://pith.science/api/pith-number/EXDOWNAVXKC2JLU3IAZ6IWDORH/graph.json","events_json":"https://pith.science/api/pith-number/EXDOWNAVXKC2JLU3IAZ6IWDORH/events.json","paper":"https://pith.science/paper/EXDOWNAV"},"agent_actions":{"view_html":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH","download_json":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH.json","view_paper":"https://pith.science/paper/EXDOWNAV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.11604&json=true","fetch_graph":"https://pith.science/api/pith-number/EXDOWNAVXKC2JLU3IAZ6IWDORH/graph.json","fetch_events":"https://pith.science/api/pith-number/EXDOWNAVXKC2JLU3IAZ6IWDORH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH/action/storage_attestation","attest_author":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH/action/author_attestation","sign_citation":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH/action/citation_signature","submit_replication":"https://pith.science/pith/EXDOWNAVXKC2JLU3IAZ6IWDORH/action/replication_record"}},"created_at":"2026-07-05T07:09:49.834710+00:00","updated_at":"2026-07-05T07:09:49.834710+00:00"}