Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A direct proof that $\ell_\infty^{(3)}$ has generalized roundness zero   Metric spaces of generalized roundness zero have interesting non-embedding
properties. For instance, we note that no metric space of generalized roundness
zero is isometric to any metric subspace of any $L_{p}$-space for which $0 < p
\leq 2$. Lennard, Tonge and Weston gave an indirect proof that
$\ell_{\infty}^{(3)}$ has generalized roundness zero by appealing to highly
non-trivial isometric embedding theorems of Bretagnolle Dacunha-Castelle and
Krivine, and Misiewicz. In this paper we give a direct proof that
$\ell_{\infty}^{(3)}$ has generalized roundness zero. This provides insight
into the combinatorial geometry of $\ell_{\infty}^{(3)}$ that causes the
generalized roundness inequalities to fail. We complete the paper by noting a
characterization of real quasi-normed spaces of generalized roundness zero.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys