Right. You are reading all that correctly.
On 11/16, the K indexes were very high (4 4 4 3 4 4 3 3). But the Kp index for that day was a 3. I don't see any correlation between the two. For yest and today, the Kp indexes were/are 4s, but the K indexes are nowhere near as high as 11/16. (2...