{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GCVRWUESZVRIPVPLEG2ALWBGWA","short_pith_number":"pith:GCVRWUES","schema_version":"1.0","canonical_sha256":"30ab1b5092cd6287d5eb21b405d826b028d2077de0f7a1cfb4f838fc4c0d7c25","source":{"kind":"arxiv","id":"1907.02171","version":2},"attestation_state":"computed","paper":{"title":"Sketched MinDist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jeff M. Phillips, Pingfan Tang","submitted_at":"2019-07-04T00:37:14Z","abstract_excerpt":"We consider sketch vectors of geometric objects $J$ through the \\mindist function \\[ v_i(J) = \\inf_{p \\in J} \\|p-q_i\\| \\] for $q_i \\in Q$ from a point set $Q$. Collecting the vector of these sketch values induces a simple, effective, and powerful distance: the Euclidean distance between these sketched vectors. This paper shows how large this set $Q$ needs to be under a variety of shapes and scenarios. For hyperplanes we provide direct connection to the sensitivity sample framework, so relative error can be preserved in $d$ dimensions using $Q = O(d/\\varepsilon^2)$. However, for other shapes, w"},"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":"1907.02171","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-07-04T00:37:14Z","cross_cats_sorted":[],"title_canon_sha256":"52cdb9d3a8680e221114b5b78726538c8ac6fa7cfa1f7b4636b7dc0edbe01ae1","abstract_canon_sha256":"7d034dbb95823f54d0c27eb9aaa25fbf69dece13ac54df21a3c9b5cabb4d202c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:16.933032Z","signature_b64":"y8cZk8ILA1qXlDuHEjXYc2ssLmlRmMPlaAODtS2XyVOQtDrPmzvwPV/XtAr+xyd3+Uy4hwxXed0e3GNCiT4yAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30ab1b5092cd6287d5eb21b405d826b028d2077de0f7a1cfb4f838fc4c0d7c25","last_reissued_at":"2026-05-17T23:41:16.932580Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:16.932580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sketched MinDist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jeff M. Phillips, Pingfan Tang","submitted_at":"2019-07-04T00:37:14Z","abstract_excerpt":"We consider sketch vectors of geometric objects $J$ through the \\mindist function \\[ v_i(J) = \\inf_{p \\in J} \\|p-q_i\\| \\] for $q_i \\in Q$ from a point set $Q$. Collecting the vector of these sketch values induces a simple, effective, and powerful distance: the Euclidean distance between these sketched vectors. This paper shows how large this set $Q$ needs to be under a variety of shapes and scenarios. For hyperplanes we provide direct connection to the sensitivity sample framework, so relative error can be preserved in $d$ dimensions using $Q = O(d/\\varepsilon^2)$. However, for other shapes, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02171","kind":"arxiv","version":2},"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":"1907.02171","created_at":"2026-05-17T23:41:16.932659+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02171v2","created_at":"2026-05-17T23:41:16.932659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02171","created_at":"2026-05-17T23:41:16.932659+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCVRWUESZVRI","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCVRWUESZVRIPVPL","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCVRWUES","created_at":"2026-05-18T12:33:18.533446+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/GCVRWUESZVRIPVPLEG2ALWBGWA","json":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA.json","graph_json":"https://pith.science/api/pith-number/GCVRWUESZVRIPVPLEG2ALWBGWA/graph.json","events_json":"https://pith.science/api/pith-number/GCVRWUESZVRIPVPLEG2ALWBGWA/events.json","paper":"https://pith.science/paper/GCVRWUES"},"agent_actions":{"view_html":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA","download_json":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA.json","view_paper":"https://pith.science/paper/GCVRWUES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02171&json=true","fetch_graph":"https://pith.science/api/pith-number/GCVRWUESZVRIPVPLEG2ALWBGWA/graph.json","fetch_events":"https://pith.science/api/pith-number/GCVRWUESZVRIPVPLEG2ALWBGWA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA/action/storage_attestation","attest_author":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA/action/author_attestation","sign_citation":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA/action/citation_signature","submit_replication":"https://pith.science/pith/GCVRWUESZVRIPVPLEG2ALWBGWA/action/replication_record"}},"created_at":"2026-05-17T23:41:16.932659+00:00","updated_at":"2026-05-17T23:41:16.932659+00:00"}