As a definition, it was originally like that, but until now, I have been interpreting this as "random thoughts" in a broad sense. However, recently, it seems that interpreting "vritti" in the Yoga Sutras as "waves" in the literal sense is the correct interpretation.

As meditation progresses and stillness deepens, one becomes aware of the subtle waves in the mind.

In fact, until recently, I didn't know that there was a state where these subtle "waves" existed, and that there was a state where these "waves" become even more still. However, I used to interpret the state where random thoughts in the mind disappear in that state where there are only slight "waves" as "the cessation of the mind (vritti, suppressing the waves)" in the Yoga Sutras.

However, that interpretation is a certain truth when meditation has not progressed much. In reality, what the Yoga Sutras define as yoga in the very first definition is, I think, exactly what the words mean.

(2) Yoga is the suppression of the modifications (vrittis) of consciousness (chitta).
"Raja Yoga" by Swami Vivekananda, p. 117

This initial definition is often interpreted as "random thoughts" or "the mind" in the general world, and I used to interpret it that way as well. This is because the Sanskrit word "chitta" represents the mind, so it has been interpreted as "stopping the voice of the mind" or "stopping thoughts." This is a kind of interpretation that "controlling the mind" is yoga, which is not entirely wrong, but I feel that it is slightly different from the essence.

When interpreted based on the idea of "stopping thoughts," the Vedanta school often criticizes the Yoga Sutras with the argument, "If you stop thinking, what do you do?" This is indeed a strange argument if you interpret it as "stopping thoughts," but there is no contradiction if you interpret it literally as "stopping the waves."

Since "vritti" literally means "waves," it refers to the "waves" that are dormant and lying beneath. These waves are basically constantly moving like the sea, and although there are slight differences in the size of the waves, they are basically always fluctuating. In general, this "wave" has been interpreted as "thoughts (thinking, random thoughts)," but that is a correct interpretation in the initial stages. However, it is probably the most accurate to interpret the meaning of the text of the Yoga Sutras directly, and I think that this "wave" means not so much "thoughts or random thoughts" but rather the "wave itself" that lies at the bottom of the mind.

Therefore, in reality, what the Vedanta school says, "whether there is thought or not, the Atman is immutable," is correct, because this "wave" continues to exist deep down, whether there is thought or not. Of course, it is possible to think in a state where the wave is calm, but it becomes correspondingly difficult to think when the wave is strong. When the wave is calm, it is possible to perceive things as they are without thinking, while, if necessary, it is also possible to think.

The fundamental principle is the same in both Yoga Sutra and Vedanta: that truth is reached when the fluctuations of the mind (vritti) are stopped. The Yoga Sutra says "cessation of the mind's modifications," while Vedanta expresses it as "antakarana suddhi" (purification of the inner self), but they are the same thing. The goal is also the same: the Yoga Sutra speaks of "Purusha" (pure observer), while Vedanta speaks of "Atman" (true self, or Brahman), and although there are many differences between the schools, in reality, they are the same thing.

When the fluctuations of the mind subside and become silent, and the waves within the mind (vritti) become even quieter, a sense of non-duality appears, and one realizes oneness, or Purusha, or Atman.

Considering this, the situation in which I thought I had achieved the "cessation of the mind's modifications" in the Yoga Sutra a while ago was actually only a glimpse, and I had not yet achieved it completely. Recently, I may finally be achieving that state to some extent.