Quadratic-Time Hardness of Furthest Pair in Superconstant Dimension
Furthest Pair and its relatives admit $f(d)\,n^{2-\Theta(1/d)}$ algorithms, making them the standard examples of barely subquadratic computation, and whether that is optimal in superconstant dimension was open. Under SETH it is: Furthest Pair requires quadratic time once the dimension is superconstant.
Exact FrontierDelta
Scope and record
Occurred: Jun 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Quadratic-Time Hardness of Furthest Pair in Superconstant Dimension · Furthest Pair under SETH
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Barna Saha
human · human collaborator
Yinzhan Xu
human · human collaborator
Christopher Ye
human · human collaborator
ChatGPT 5.5 Pro (with Codex, Claude Opus, Gemini for feedback)
model · ai model contributor · OpenAI / Anthropic / Google
Lineage and corrections
This event attributed to Christopher Ye
This event attributed to Yinzhan Xu
This event attributed to Barna Saha
This event attributed to ChatGPT 5.5 Pro (with Codex, Claude Opus, Gemini for feedback)