We see no mention of any information in the scans presented for this, but only how each Magic Formula is a different spell... Yeah, that's literally how all magic works...
And if you wanna argue for it, you need much more evidence than this, with them at least mentioning "information," other than just different magical formulas having different results (Spells), since this is no different than every other magic from every other verse that uses chants or symbols for their own magic, where the different chats/symbols results in a different result (spell).
Information doesn't have to be stated, not using typical powerscaling jargon doesn't mean it cannot be reasoned to be information. It's the same as saying "unless "concept", is mentioned it isn't conceptual manipulation".
On the other hand, there's something wrong in your argument. Concentrating on the parts I bolded, the reasoning was never "each magic formula is a different spell", the generalization too is also out of place.
Yes different magic verses use chants and symbols that's common place however, runes, chants, symbols etc. cannot be generalized to spell formula, they can only be generalized to magic/ spell circles. A spell formula is an underlining practical and theoretical formula, the core of a spell that dictates it's function. It's a fundamental component in it. Using a simplified process "Draw magic circle>shoot fire", the fire released would've have it's underlying spell formula at the core which enables it to function.
There's nothing manipulating information, though. It's like calling chemistry information manipulation, because chemistry follows the exact same premise- if you change the formula, you get a different result. This is a nothingburger of a justification, it is strictly expose on how the magic works.
No offense intended but this is a poor comparison. A chemical formula or even mathematical formulas in general are just symbols used to express, the structure of compounds, rules on how elements interact. Writing out and editing a chemical formula doesn't change how one element would react with another but on the other hand, manipulating spell formulae would manipulate and determine a spell's properties, function and how they interact with each other.
The magic itself isn't information or analogous to it- or if it is, you've been wasting time arguing about the presence of the formulae being the justification for information manip. So whatever magic is, changing the formula of it doesn't render it information manipulation. No information is in fact manipulated. Just the means of creating the magic is, thus yielding a different result. That's just like. How things tend to work. In real life, and in this fictional verse.
Magic itself was never information though just the spell formula/core underlying in it. Changing that formula regardless of what it is would infact be the manipulation of it no? You're also misunderstanding, the means of creating magic is the magic/spell circle that too can be manipulated as well but it doesn't fundamentally change the spell.
I'm pretty sure reality on page refers to the reality of the universe in verse. And you're right, it is necessary, but that information can just be knowledge, doesn't have to be the building blocks of reality.
Except knowledge isn't the core of something neither can it alter it. A part of reality is still reality either way isn't it?
Something being a possible use of an ability does not mean that having that grants the ability. E.g. a possible use of plot manipulation is altering concepts, but that does not mean that you get plot manipulation just by altering concepts. You actually have to meet all the requirements for plot manipulation independently of that feat.
It's basically confusing cause and effect. The same effect can be achieved by many causes.
Isn't that kind of backwards? It wouldn't be a possible use in this case, since it is said to be "formulae" but I do understand what you're saying.
Unless it's like Kawakami-verse and all of reality is composed of magic formulas that doesn't work. From what I see magic formulas here are just the thing giving magic structure, not things that define the fundamental nature of matter and energy as a whole. (i.e. not fundamental building blocks of reality)
This seems to also fall under what you said above. For the verse you outlined, magic formula's are information, in that case, there's no question that something described as "magic formulas" are in fact information the only difference being how they affect reality however, simply defining reality isn't what makes them information. In this case, a spell is still a part of reality, that doesn't change so rather than removing it entirely, I would rather say it should be limited. Consequently, you're also saying if information subsists as a fundamental aspect of a part of reality but not all of it then it isn't information manipulation.
All the scans say at the end of the day is that "if you change how you do it, you get a different effect; we have documented how to get certain effects, and if you do it differently, you will not get the same result". Info Manip is straight up not here man.
Except that's not what it says and it's still you asserting your stance with the example of chemical formula.
NaCl + H²O= NaOH + HCl.
Changing the formula above to NaCl + H²O= H²SO⁴ doesn't affect how sodium chloride would react with water, sulphuric acid will never be the resultant of their mixture, I've only succeeded at writing something incomprehensible. The reverse however will be the case with spell formula if it is altered even without the addition of compounds that would result in the formation of sulphuric acid.
These arguments have already been debunked and debated in this thread.
Something is debunked when you've disproven the claim, all you've done is misinterpret by conflating spell formula as magic circles and generalizing it with other works of fiction.