How to assess The Federalist Papers' authorship with statistics

The Federalist Papers comprises of 85 articles written in the 1780s by founding fathers Alexander Hamilton, James Madison and John Jay. They wrote under a collective pseudonym, Publius, so keep their involvement secret. But who wrote what? There is much dispute. Let's try K-Means Clustering.

K-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. For our example we'll have 68 observations (papers) into 2 clusters (2 authors, Madison and Hamilton).

Once the data has been converted into workable features, we can fit them onto a 2-cluster model. This is unsupervised - we are effectively just pouring in our (ideally) significant data and telling it that there are two distinct sets within it, and to try and extricate them.

Spoiler: most of them were by Hamilton.