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This article derives lower bounds on the supremal (strict) p-negative type offinite metric spaces using purely elementary techniques. The bounds depend onlyon the cardinality and the (scaled) diameter of the underlying finite metricspace. Examples show that these lower bounds can easily be best possible underclearly delineated circumstances. We further point out that the entire theoryholds (more generally) for finite semi-metric spaces without modification andwherein the lower bounds are always optimal.

Optimal lower bounds on the maximal p-negative type of finite metric spaces