Quote from: Mahouka Koukou no Rettousei:Volume 8 Chapter 3
“It’s the Kuroba elder sister and younger brother.”
Every member of yotsuba have unique power that is impossible to categorized with modern magic, most probably obtained(fixed marriages) and maintained via bloodline.
Not sure why you think this. Every Yotsuba magic I've seen has been categorised using the modern magic system. Along with the systematic magic groups, the groups of systematic-type exceptions of perception magic, non-systematic magic and outer-systematic magic are all part of the modern magic categorisation system.
Maya's magic is described as Convergence type Systematic magic in V8, Miyuki's and Miya's and Fumiya's are Outer-Systematic magic, Ayako's is Weight and Convergence Systematic-type and Tatsuya describes his decomposition magic as a part of the Separation systematic magic.
Those are their innate abilities that defy currently known logic, rules for magic and are impossible to recreate even with 16 building blocks of cardinal code which is Tatsuya analysis of them.
The categorisation of modern magic includes the exceptions to systematic magic and is not based on any fundamental magic rules or the cardinal codes. The modern magic categorisation system is described in V1 as being based generally on the type and effect the magic has after its cast.
It's true nature is undisclosed and we don't know how, why or even if it changes via inheritance(there are no even remote similarities for Miyuki, Tatsuya and Miya).
We actually do get alot of info about Yotsuba inherited magic from the V8 SS shown in spoilers given previously.
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Cocytus seems to be only limited magical aplication of that ability(like mb is aplication of decomposition) the same way like symptoms of freezing magic is manifestation of it in physical dimension.
Cocytus shouldn't really be described as limited since its just the name of a specific spell like Inferno or Gram Demolition. Its just the ultimate offensive version of Miyuki's special outer-systematic talent. We know she can also use this innate ability for suppressing one's magic, like she does to prevent magicians seeing Tatsuya's normally overwhelming aura of psion light. But we haven't been given a specific name for this skill other than it being from mental interference magic.
Me using physics and 8types/4systems knowledge for cognition of toll used to alter reality is irrevelant to the topic ...
Well I apologise if I originally misunderstood your question. I thought you could not understand how mental interference could be used to affect a molecule's vibration. But if you were actually asking how magic from that falls in the outer-systematic category can freeze things like magic in the Systemic Vibration category then, that has to do with how modern magic is categorised.
Since modern magic classification is mainly based on what result the magic brings about, it can be quite fluid. The first example we got is the magic Tatsuya used against Hanzo in V1 being described as having both Non-systematic and Vibration-Systematic properties, even though psions are not molecules. We also have cases of Tatsuya Decomposition magic and Miyuki's Freezing magic that depending on the targets fall within different categories(for Miyuki, outer-systematic for non-material bodies and systematic vibration for material bodies; for Tatsuya it's non-systematic for magic sequences and Systematic Decomposition, a sub category of Systematic Separation, for Mist Dispersal which targets material bodies).