centum

We can provide an example from the centum side; Latin (and English) preserve the nasal (ceNtum / huNdred) but Greek does not (heka_ton).

Such a division is made particularly unlikely by the discovery that while the satem group lies generally to the east and the centum group to the west, the most eastward of the known IE language branches, Tocharian, is centum.

Latin is from th centum branch and Sanskrit is from the satem branch (which includes Proto-Slavic as well).

To throw further confusion into it, both hundred[1] and centum[2] came from the same Proto-Indo-European word *ḱm̥tóm.

That said, most of the centum languages to this day are western languages and most of the satem are eastern.

Are there centum languages that merged k into ḱ rather than the other way around?

The IE languages are usually divided into two groups: the *centum and *satem languages.

However, the discovery of Tocharian changed this situation: Tocharian was the easternmost of all early IE languages, yet was a centum language!

I still don't understand why Tocharian being centum in the east would be considered to contradict the theory that the centum/satem split was one ancestral innovation as opposed to many independent innovations.

You may note that this seems very much like an east/west division, with centum languages in the west and satem languages in the east.

The big exceptions are Slavic (satem), Mittani (satem), and Tocharian (centum).

For example, Latin /k/ is often German /h/ (canis/Hund, centum/hundert, cordis/Herz, cornus/Horn).

Why does the geography of Tocharian matter to the hypothesis that centum / satem reflects an early split between "proto-centum" and "proto-satem"?

But it's a ratio to a standard 100 … and that's literally what a percentage is ("per centum" = "by the hundred").

Eight eggs is 0.8 of a dozen, 0.08 of a gross, or 8 "pg", per-gross, akin to per-centum.

Mao was very fond of the Latin "Unum castigabis, centum emendates".