(Attempted) Analysis of Petrification Spell [MANGA SPOILERS; BE WARNED!]
I started looking at the petrify spell, and I have a partial theory as to how it works - please do tell me if I get anything wrong, if you have other interpretations or if there's just anything you disagree with!
I've highlighted every sign/sigil we've seen before (apologies if I missed any!), and they seem to redirecting whatever the spell is doing outwards. The bend signs could indicate that the spell is being cast in a sort of vortex, similar to the Whorling Winds sigil (there are other reasons that support this - I'll bring them up later).
Here I've also noticed some glaives that appear to be a part of some larger structure - these could be a more powerful version of glaives maybe? They likely have the same function given the context of the spell.
I'm gonna mostly ignore the center sigil, and I'll just assume it allows for creation and manipulation of the unknown material.
These parts look suspiciously similar to the crystal sigil, which would make sense - especially if the substance the central sigil produces doesn't naturally form a crystalline structure. My headcanon is that it's just the Brimmed Caps being flashy for Coco's sake.
Now, these four outer parts - I believe they ought to be read in clockwise order, starting at the top. This is for two reasons:
That's the only way I could make them make sense given the spell's effect
These signs:
They show up on all four outer semicircles, and seem to show which semicircle to go to next. However, this assumes that spells read clockwise by default, which there is no evidence to confirm as far as I know.
Let's start with the top one: it seems to create a fluid of some kind. I say this because similar wavy patterns have only been seen in sigils (and one sign that I know of) that affect air and water - the two fluid elements. This is likely to enable the spell to flow before turning to crystal.
The right-hand one looks similar to the Whorling Winds sigil I mentioned earlier, and so it's not unreasonable to assume it has a similar effect - rotating this fluid around and spreading it evenly outward.
Now the bottom one - it's just a time stop spell.
Time stop/reverse spell (for reference)
This is probably to preserve Coco's mother and keep her alive, as the entire point of this (as far as I can tell) is to try and convince Coco to use forbidden magic intentionally, similarly to what the Brimmed Caps did with Euini.
The left-hand one seems to be doing something to compress the fluid - likely turning it back into that crystal we saw, or at least into a solid.
That's all, apologies if it seems a bit far fetched (I only just came up with it lol), and also apologies if I'm just repeating things that have been stated in the manga (not fully caught up) or that someone else has already figured out!
(oh, and the spell illustration is from https://witchhatatelier.telepedia.net, as is a lot of my info)