Is there any special reason to use the character "k" standing for the "early"?

Question

From the paper of Bacon,2018, p.5, I saw a paragraph as below

The simplest way to illustrate how treatment timing works is to consider a balanced panel dataset with 𝑇 periods (𝑡) and 𝑁 cross-sectional units (𝑖) that belong to either an untreated group, 𝑈; an early treatment group, 𝑘, which receives a binary treatment at 𝑡 * 𝑘; and a late treatment group, ℓ, which receives the binary treatment at 𝑡 * ℓ > 𝑡 * 𝑘

In this paragraph, I am curious if "k" stand for any word having the meaning "early". For example, "l" is late, "U" is untreated,...

Answer 1

You can write the author to know for sure, without this one can only speculate.

I don't think the solution is that there is a word for early that starts with a k. Rather people do not like to use $e$, as it has a meaning as Euler's number, while $i,j,k,l$ are pretty standard indexing letters.