{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:M63RUUFDS74L56SFEU62TFWHK6","short_pith_number":"pith:M63RUUFD","schema_version":"1.0","canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","source":{"kind":"arxiv","id":"1810.04321","version":1},"attestation_state":"computed","paper":{"title":"The Andoni--Krauthgamer--Razenshteyn characterization of sketchable norms fails for sketchable metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.FA","math.MG"],"primary_cat":"cs.DS","authors_text":"Assaf Naor, Subhash Khot","submitted_at":"2018-10-10T00:56:59Z","abstract_excerpt":"Andoni, Krauthgamer and Razenshteyn (AKR) proved (STOC 2015) that a finite-dimensional normed space $(X,\\|\\cdot\\|_X)$ admits a $O(1)$ sketching algorithm (namely, with $O(1)$ sketch size and $O(1)$ approximation) if and only if for every $\\varepsilon\\in (0,1)$ there exist $\\alpha\\geqslant 1$ and an embedding $f:X\\to \\ell_{1-\\varepsilon}$ such that $\\|x-y\\|_X\\leqslant \\|f(x)-f(y)\\|_{1-\\varepsilon}\\leqslant \\alpha \\|x-y\\|_X$ for all $x,y\\in X$. The \"if part\" of this theorem follows from a sketching algorithm of Indyk (FOCS 2000). The contribution of AKR is therefore to demonstrate that the mere "},"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":"1810.04321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-10T00:56:59Z","cross_cats_sorted":["cs.CG","math.FA","math.MG"],"title_canon_sha256":"447fab118f675a23ad64579dcba2db52b4f8646023bb93d89f9fcfbdcb295c2a","abstract_canon_sha256":"19301ae29481082bc3a97f771ca94c72be8b1fb4963866716528bbf54c04b4d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:40.395519Z","signature_b64":"OisGemf09WZDkf4Q8OJpYu78zvH73IG+KyeiMtGhacwqYJmgh5yMmkuoRFbo5sv6mBXCEwd9KPpuGf284oQACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67b71a50a397f8befa45253da996c757826c2e49d6d25e06dc1cc3f29cd7d2aa","last_reissued_at":"2026-05-18T00:03:40.395044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:40.395044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Andoni--Krauthgamer--Razenshteyn characterization of sketchable norms fails for sketchable metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.FA","math.MG"],"primary_cat":"cs.DS","authors_text":"Assaf Naor, Subhash Khot","submitted_at":"2018-10-10T00:56:59Z","abstract_excerpt":"Andoni, Krauthgamer and Razenshteyn (AKR) proved (STOC 2015) that a finite-dimensional normed space $(X,\\|\\cdot\\|_X)$ admits a $O(1)$ sketching algorithm (namely, with $O(1)$ sketch size and $O(1)$ approximation) if and only if for every $\\varepsilon\\in (0,1)$ there exist $\\alpha\\geqslant 1$ and an embedding $f:X\\to \\ell_{1-\\varepsilon}$ such that $\\|x-y\\|_X\\leqslant \\|f(x)-f(y)\\|_{1-\\varepsilon}\\leqslant \\alpha \\|x-y\\|_X$ for all $x,y\\in X$. The \"if part\" of this theorem follows from a sketching algorithm of Indyk (FOCS 2000). The contribution of AKR is therefore to demonstrate that the mere "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04321","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":"1810.04321","created_at":"2026-05-18T00:03:40.395119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04321v1","created_at":"2026-05-18T00:03:40.395119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04321","created_at":"2026-05-18T00:03:40.395119+00:00"},{"alias_kind":"pith_short_12","alias_value":"M63RUUFDS74L","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"M63RUUFDS74L56SF","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"M63RUUFD","created_at":"2026-05-18T12:32:37.024351+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/M63RUUFDS74L56SFEU62TFWHK6","json":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6.json","graph_json":"https://pith.science/api/pith-number/M63RUUFDS74L56SFEU62TFWHK6/graph.json","events_json":"https://pith.science/api/pith-number/M63RUUFDS74L56SFEU62TFWHK6/events.json","paper":"https://pith.science/paper/M63RUUFD"},"agent_actions":{"view_html":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6","download_json":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6.json","view_paper":"https://pith.science/paper/M63RUUFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04321&json=true","fetch_graph":"https://pith.science/api/pith-number/M63RUUFDS74L56SFEU62TFWHK6/graph.json","fetch_events":"https://pith.science/api/pith-number/M63RUUFDS74L56SFEU62TFWHK6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/action/storage_attestation","attest_author":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/action/author_attestation","sign_citation":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/action/citation_signature","submit_replication":"https://pith.science/pith/M63RUUFDS74L56SFEU62TFWHK6/action/replication_record"}},"created_at":"2026-05-18T00:03:40.395119+00:00","updated_at":"2026-05-18T00:03:40.395119+00:00"}