{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2IEXBN6MZTKCOLNZ2MOIDHWCPE","short_pith_number":"pith:2IEXBN6M","schema_version":"1.0","canonical_sha256":"d20970b7ccccd4272db9d31c819ec2793b39c15b5760cc5030c6c5ab50b37d1a","source":{"kind":"arxiv","id":"2601.15470","version":3},"attestation_state":"computed","paper":{"title":"Bi-Lipschitz extensions and outlier embeddings into trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arnold Filtser, Kristin Sheridan, Shuchi Chawla, Yoni Trachtenberg","submitted_at":"2026-01-21T21:09:18Z","abstract_excerpt":"We develop low distortion embeddings with outliers from arbitrary metrics into hierarchically separated trees (HSTs). In particular, we develop an efficient algorithm that for any $\\epsilon>0$, given an input metric $(X,d)$, and a probabilistic embedding of all but $k$ points from $X$ into HSTs with distortion $c$, samples from a probabilistic embedding of all but $O(\\frac{k}{\\epsilon}\\log k)$ points into HSTs that achieves distortion at most $(32+\\epsilon)c$.\n  Our results are based on two key technical components. First, we extend an algorithm of Munagala et al. [2023] for minimizing the dis"},"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":"2601.15470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-01-21T21:09:18Z","cross_cats_sorted":[],"title_canon_sha256":"f70d843ef44489e722d87aa0ec97e0178242df4a3413ce90e917e6bae64fb163","abstract_canon_sha256":"cc555627d9e6178631eda62abcf88bfc3384dd2bf752b3dcd341cc39593c0159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T00:18:12.396126Z","signature_b64":"LQimBYWd6uK70BbtToC9JLpqlw4WiIM0RU0GBzhPVRQjSdhHjmj46zQJ1mmeeqzugmPc2c82V6rUZ0hxt/mLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d20970b7ccccd4272db9d31c819ec2793b39c15b5760cc5030c6c5ab50b37d1a","last_reissued_at":"2026-06-25T00:18:12.395680Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T00:18:12.395680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bi-Lipschitz extensions and outlier embeddings into trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arnold Filtser, Kristin Sheridan, Shuchi Chawla, Yoni Trachtenberg","submitted_at":"2026-01-21T21:09:18Z","abstract_excerpt":"We develop low distortion embeddings with outliers from arbitrary metrics into hierarchically separated trees (HSTs). In particular, we develop an efficient algorithm that for any $\\epsilon>0$, given an input metric $(X,d)$, and a probabilistic embedding of all but $k$ points from $X$ into HSTs with distortion $c$, samples from a probabilistic embedding of all but $O(\\frac{k}{\\epsilon}\\log k)$ points into HSTs that achieves distortion at most $(32+\\epsilon)c$.\n  Our results are based on two key technical components. First, we extend an algorithm of Munagala et al. [2023] for minimizing the dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.15470","kind":"arxiv","version":3},"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/2601.15470/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":"2601.15470","created_at":"2026-06-25T00:18:12.395739+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.15470v3","created_at":"2026-06-25T00:18:12.395739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.15470","created_at":"2026-06-25T00:18:12.395739+00:00"},{"alias_kind":"pith_short_12","alias_value":"2IEXBN6MZTKC","created_at":"2026-06-25T00:18:12.395739+00:00"},{"alias_kind":"pith_short_16","alias_value":"2IEXBN6MZTKCOLNZ","created_at":"2026-06-25T00:18:12.395739+00:00"},{"alias_kind":"pith_short_8","alias_value":"2IEXBN6M","created_at":"2026-06-25T00:18:12.395739+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE","json":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE.json","graph_json":"https://pith.science/api/pith-number/2IEXBN6MZTKCOLNZ2MOIDHWCPE/graph.json","events_json":"https://pith.science/api/pith-number/2IEXBN6MZTKCOLNZ2MOIDHWCPE/events.json","paper":"https://pith.science/paper/2IEXBN6M"},"agent_actions":{"view_html":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE","download_json":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE.json","view_paper":"https://pith.science/paper/2IEXBN6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.15470&json=true","fetch_graph":"https://pith.science/api/pith-number/2IEXBN6MZTKCOLNZ2MOIDHWCPE/graph.json","fetch_events":"https://pith.science/api/pith-number/2IEXBN6MZTKCOLNZ2MOIDHWCPE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE/action/storage_attestation","attest_author":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE/action/author_attestation","sign_citation":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE/action/citation_signature","submit_replication":"https://pith.science/pith/2IEXBN6MZTKCOLNZ2MOIDHWCPE/action/replication_record"}},"created_at":"2026-06-25T00:18:12.395739+00:00","updated_at":"2026-06-25T00:18:12.395739+00:00"}