Solar breathing: the original technique
I want to start this discussion with a disclaimer: All information in this article comes from Episode 6 of the Entertainment District Arc. If we learn more about breathing techniques after this date, then all the better. But this new information will not be repeated in this article.
And, given that Sun Breathing was revealed in the series after I planned to write this post, I believe it is safe to assume that more information will be disclosed in the future. I had intended to talk only about the other breathing techniques. Shinjuro Rengoku reveals that Sun Breathing was the first breathing technique in Episode 1 of the Entertainment District arc.

He also claims that all other breathing techniques are mere imitations of Sun Breathing.
This is crucial information that was revealed at the start of season two. It teaches us that Sun Breathing is the pinnacle of breathing techniques, with all others being poor imitations. It can, however, provide a look into the conflict between demons and demon slayers. Take into account the following: Sunlight destroys demons, and the sun breathing technique is the first demon-killing technique. Is this a coincidence? Most likely not. (Demons also work at night, and their higher echelons are referred to as the Twelve Demon Moons.) The question is whether the technique is called Sun Breathing because it destroys demons in the same way the sun does or because it uses the sun’s power. Both solutions are viable at this time. It’s still unclear whether the breathing techniques produce “magic” or if what we perceive is merely a visual effect.
Relation table between breathing techniques
The Mugen Train arc provided us with a breathing method relationship chart, which prompted me to write about it. Rengoku, RIP, demonstrates to Tanjiro how the majority of breathing techniques are interconnected.

However, two techniques are missing from the table presented to us. Naturally, the sun’s breath isn’t mentioned because it hasn’t been officially revealed yet. And, of course, Rengoku didn’t know.
The other technique not listed in the chart is Breath of the Beast, the technique used by Inosuke. So we don’t know where it is. But it is also possible that it has nothing to do with the other techniques.
I don’t remember how Inosuke learned this technique. But it is possible that it is an original technique that was developed independently of the others.
According to Rengoku , there are five main breathing techniques. They are flame, water, wind, stone and thunder. And as basic techniques, they are the closest to the Breath of the Sun. If the breath of the sun is first generation, these techniques are second generation.

Beyond these five techniques, there are also third generation techniques. The breath of love is derived from flame, the serpent and flower are derived from water, the mist is derived from wind, and the sound is derived from thunder. No known technique branches out from stone breathing.
There is also only one fourth generation technique that we know of: Insect Breathing. According to the painting, the insect technique derives from the flower technique. And I feel like it was mentioned in Shinobu’s story in the first season.
As for the place of beast breath, I would say it is a branch of water breath. All derivatives of Water Breathing have to do with living creatures. And, as far as I can tell, “beast” refers to live things.
Is there a hierarchy in breathing techniques?
It appears that there is a definite hierarchy when we consider that we know there is an original breathing technique and three further evolved generations (at least) of techniques. However, I’m not certain that this is the case. We can assume that there is a hierarchy between the Sun Breathing technique and the other techniques based on Shinjuro’s words.

The Solar Breath seems to be clearly above the others. However, we don’t yet know how this will effect things. Is it for some reason easier to slay demons using Sun Breath? Aside from that, I don’t believe there is much of a hierarchy. After all, have a look at the nine Hashira’s breathing techniques.
There are four second-generation members, four third-generation members, and one fourth-generation member. If the further a method is from Sun Breathing, the weaker it is, so Insect Breathing Hashira is unlikely to exist.
That said, I can also argue for the existence of a hierarchy of breathing techniques. And this argument rests on two “proofs”.
First, Rengoku tells Tanjirou that throughout the ages there has always been a Hashira of flame and water (until he died). One would assume that there has always been a Flame Hashira and a Water Hashira simply because they are two of the most powerful techniques. Naturally, users of these techniques are strong enough to become Hashira.
Second, the only Insect Breathing technique user we know of is Shinobu, who uses a modified blade to deliver toxins. I believe the explanation originally given was that Shinobu just isn’t physically strong enough to behead demons so she has to kill them that way.
But, what if the reason she’s not strong enough is because she’s using a fourth generation breathing technique? This would mean that Shinobu had to overcome a lot to become a Hashira.

Conclusion
Hopefully, we’ll find out where Beast’s Breath falls in the skill chart soon. And, perhaps there are additional techniques that have not yet been revealed. I would like to see what a derivative of Stone Breathing would be like.
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