Gorman's peel restriction conjecture for finite metric spaces

Let dd be a metric of strict negative type on a finite space, let I\mathcal{I} be a subset of peel⁡(d)\operatorname{peel}(d), and let d∣Id|_{\mathcal{I}} denote the restriction of dd to I\mathcal{I}. Gorman's peel restriction conjecture. If dd is strict negative type on a finite space and I⊆peel⁡(d)\mathcal{I} \subseteq \operatorname{peel}(d), then

peel⁡(d∣I)=I.\operatorname{peel}(d|_{\mathcal{I}})=\mathcal{I}.

This claim is disproved by the displayed four-point metric in the paper: although dd has strict negative type and peel⁡(d)=[4]\operatorname{peel}(d)=[4], one has peel⁡(d∣[3])={2,3}≠[3]\operatorname{peel}(d|_{[3]})=\{2,3\}\ne[3].

References

Primary source

Steve Huntsman, “Peel neighborhoods”, arXiv:2603.26645 (2026).

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