{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BTQ5IE5W4CBRGX6CGRGXKTWDCY","short_pith_number":"pith:BTQ5IE5W","schema_version":"1.0","canonical_sha256":"0ce1d413b6e083135fc2344d754ec3162d81746f1b2d08c526e88cc4b44df90a","source":{"kind":"arxiv","id":"1012.2307","version":1},"attestation_state":"computed","paper":{"title":"Assouad's theorem with dimension independent of the snowflaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Assaf Naor, Ofer Neiman","submitted_at":"2010-12-10T16:06:24Z","abstract_excerpt":"It is shown that for every $K>0$ and $\\e\\in (0,1/2)$ there exist $N=N(K)\\in \\N$ and $D=D(K,\\e)\\in (1,\\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\\e})$ admits a bi-Lipschitz embedding into $\\R^N$ with distortion at most $D$. The classical Assouad embedding theorem makes the same assertion, but with $N\\to \\infty$ as $\\e\\to 0$."},"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":"1012.2307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-12-10T16:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"e42186cfedf9868bd6acf9f57f3b6bfa27a18f787cdd62931ae66e1c52153492","abstract_canon_sha256":"9c24de1fea2004080f2fa5d7055fad75dddbb693e8e72b6284deee48230a4d88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:38.101806Z","signature_b64":"h1KNyn4KihShfMUzwPY3U2TGkdT50SEgs1SO0JZkXzpBy7YCd3y2azd6a9sykMt/7zvy9GccfrYIgEmElorLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ce1d413b6e083135fc2344d754ec3162d81746f1b2d08c526e88cc4b44df90a","last_reissued_at":"2026-05-18T04:33:38.101223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:38.101223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Assouad's theorem with dimension independent of the snowflaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Assaf Naor, Ofer Neiman","submitted_at":"2010-12-10T16:06:24Z","abstract_excerpt":"It is shown that for every $K>0$ and $\\e\\in (0,1/2)$ there exist $N=N(K)\\in \\N$ and $D=D(K,\\e)\\in (1,\\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\\e})$ admits a bi-Lipschitz embedding into $\\R^N$ with distortion at most $D$. The classical Assouad embedding theorem makes the same assertion, but with $N\\to \\infty$ as $\\e\\to 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2307","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1012.2307","created_at":"2026-05-18T04:33:38.101285+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2307v1","created_at":"2026-05-18T04:33:38.101285+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2307","created_at":"2026-05-18T04:33:38.101285+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTQ5IE5W4CBR","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTQ5IE5W4CBRGX6C","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTQ5IE5W","created_at":"2026-05-18T12:26:05.355336+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/BTQ5IE5W4CBRGX6CGRGXKTWDCY","json":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY.json","graph_json":"https://pith.science/api/pith-number/BTQ5IE5W4CBRGX6CGRGXKTWDCY/graph.json","events_json":"https://pith.science/api/pith-number/BTQ5IE5W4CBRGX6CGRGXKTWDCY/events.json","paper":"https://pith.science/paper/BTQ5IE5W"},"agent_actions":{"view_html":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY","download_json":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY.json","view_paper":"https://pith.science/paper/BTQ5IE5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2307&json=true","fetch_graph":"https://pith.science/api/pith-number/BTQ5IE5W4CBRGX6CGRGXKTWDCY/graph.json","fetch_events":"https://pith.science/api/pith-number/BTQ5IE5W4CBRGX6CGRGXKTWDCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY/action/storage_attestation","attest_author":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY/action/author_attestation","sign_citation":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY/action/citation_signature","submit_replication":"https://pith.science/pith/BTQ5IE5W4CBRGX6CGRGXKTWDCY/action/replication_record"}},"created_at":"2026-05-18T04:33:38.101285+00:00","updated_at":"2026-05-18T04:33:38.101285+00:00"}