Year: 2026
Type: preprint
Abstract: For every integer $k\ge1$, we prove that each nonempty bounded set in real $\ell_1^{4k+1}$ has an ambient enclosing ball of radius at most $(4k-1)/(4k)$ times its diameter. The bound is sharp in dimension five: $J(\ell_1^5)=3/4$. If a Hadamard matrix of order $4k$ exists, then $J(\ell_1^{4k-1})=J(\ell_1^{4k})=J(\ell_1^{4k+1})=(4k-1)/(4k)$. The upper bound for every $k\ge1$ has been formalized in Lean.
Source: arXiv (Cornell University)
Author: Li, Xiao
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220982926