{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2YR4WGEMUWOTANFG5NPAWDQGIO","short_pith_number":"pith:2YR4WGEM","schema_version":"1.0","canonical_sha256":"d623cb188ca59d3034a6eb5e0b0e064384ec29aa3f21349868dc41c4e327b925","source":{"kind":"arxiv","id":"2606.25887","version":1},"attestation_state":"computed","paper":{"title":"Furthest Pair Requires Quadratic Time in Superconstant Dimension under SETH","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.CG","authors_text":"Barna Saha, Christopher Ye, Yinzhan Xu","submitted_at":"2026-06-24T14:29:47Z","abstract_excerpt":"Several fundamental problems in computational geometry admit algorithms with running time $f(d) \\cdot n^{2-\\Theta(1/d)}$ for $n$ points in $d$ dimensions, making them among the most prominent examples of barely subquadratic computation. Notable members of this class include Furthest Pair, Bichromatic Closest Pair, (Bichromatic) Maximum Innter Product, and Hopcroft's Problem. Chen [Theory Comput. 2020] proved that, assuming the Strong Exponential Time Hypothesis (SETH), these problems require $n^{2-o(1)}$ time when the dimension satisfies $d=2^{\\Theta(\\log^* n)}$. We extend this lower bound to "},"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":"2606.25887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-24T14:29:47Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"15732ffba315c6367109a8b8a4f62bebe16e4aa7abebc6e240c08994ca6984fd","abstract_canon_sha256":"8fcc89adf444366ab71f6ed173d8bc1bc30d8b6423fcbfd6e57d3d66619b8470"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:42.312439Z","signature_b64":"+l9O0BbfqsF0hUv6E0uX71SV/nuXzjZR/PrubRNIMvOezRbfN5MatQOTsV5NdEh2oW2+vk/J7+Wdiz77LH5wDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d623cb188ca59d3034a6eb5e0b0e064384ec29aa3f21349868dc41c4e327b925","last_reissued_at":"2026-06-25T01:18:42.312092Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:42.312092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Furthest Pair Requires Quadratic Time in Superconstant Dimension under SETH","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.CG","authors_text":"Barna Saha, Christopher Ye, Yinzhan Xu","submitted_at":"2026-06-24T14:29:47Z","abstract_excerpt":"Several fundamental problems in computational geometry admit algorithms with running time $f(d) \\cdot n^{2-\\Theta(1/d)}$ for $n$ points in $d$ dimensions, making them among the most prominent examples of barely subquadratic computation. Notable members of this class include Furthest Pair, Bichromatic Closest Pair, (Bichromatic) Maximum Innter Product, and Hopcroft's Problem. Chen [Theory Comput. 2020] proved that, assuming the Strong Exponential Time Hypothesis (SETH), these problems require $n^{2-o(1)}$ time when the dimension satisfies $d=2^{\\Theta(\\log^* n)}$. We extend this lower bound to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25887","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25887/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":"2606.25887","created_at":"2026-06-25T01:18:42.312147+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25887v1","created_at":"2026-06-25T01:18:42.312147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25887","created_at":"2026-06-25T01:18:42.312147+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YR4WGEMUWOT","created_at":"2026-06-25T01:18:42.312147+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YR4WGEMUWOTANFG","created_at":"2026-06-25T01:18:42.312147+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YR4WGEM","created_at":"2026-06-25T01:18:42.312147+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/2YR4WGEMUWOTANFG5NPAWDQGIO","json":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO.json","graph_json":"https://pith.science/api/pith-number/2YR4WGEMUWOTANFG5NPAWDQGIO/graph.json","events_json":"https://pith.science/api/pith-number/2YR4WGEMUWOTANFG5NPAWDQGIO/events.json","paper":"https://pith.science/paper/2YR4WGEM"},"agent_actions":{"view_html":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO","download_json":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO.json","view_paper":"https://pith.science/paper/2YR4WGEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25887&json=true","fetch_graph":"https://pith.science/api/pith-number/2YR4WGEMUWOTANFG5NPAWDQGIO/graph.json","fetch_events":"https://pith.science/api/pith-number/2YR4WGEMUWOTANFG5NPAWDQGIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO/action/storage_attestation","attest_author":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO/action/author_attestation","sign_citation":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO/action/citation_signature","submit_replication":"https://pith.science/pith/2YR4WGEMUWOTANFG5NPAWDQGIO/action/replication_record"}},"created_at":"2026-06-25T01:18:42.312147+00:00","updated_at":"2026-06-25T01:18:42.312147+00:00"}