Well, if you are willing to pay for that extra magnitude compared to T:Group, and do not care about spontaneous uses for it (unlikely anyway, given +4 Arc, +2 Group, +1 "special") then you need no breakthrough at all -- see ArM5 p.114.
I think there's an excessive tendency to cry "breakthrough" for everything
My group has a bunch of "Breakthroughs" that were in effect when the campaign started, which are in effect House Rules. One of those is it only taking a week to fix an AC (and it being able to be done as a 7 day distraction during other lab activity).
But yes requiring a "breakthrough" for everything can be a problem from some groups. Lots of things that this is used for can actually be done by careful manipulation of RAW. Continuous effects for example. While D: Sun, 2/day, and E. Trigger are the "standard" way, there are several others. They might not be as efficient, but can still be done.
Be careful here, because that's incorrect. Yes, creo spells create something. Yes, the target is the number of instances or size of what is being created. No, Arcane connection isn't a target parameter. Arcane Connection is a range parameter. Therefore, a Creo Ignem spell burning something at arcane connection range is just as legal as a pilum of fire burning a target at voice range. There is nothing in the arcane connection range that requires a Wizard's Tunnel to allow it. The purpose of the wizard's tunnel is to use your touch and voice range spell at arcane connection range and therefore boost your magic to function at a higher magnitude than it was learned at which is the purview of Muto Vim. It is in no way shape or form mandatory to use Wizard's Tunnel to enable Creo spells at arcane connection range. It is merely a more difficult effect. Likewise, there is nothing inherently prohibiting an arcane connection spell to target a group.
True, it should be quite possible to invent a spell to target through a group of Arcane Connections, or make enchanted items using such a Target. One extra magnitude seems reasonable.
The breakthrough would only be needed if you wanted to use that new target with spontaneous casting, or with Flexible Formulaic Magic, or similar.
Be careful there, because you are misrepresenting what I wrote. If you affect something by making it hotter (Creo Ignem) it's fine to do it at R:Arc. But can you create, say, a cat close to a person to which you have an Arcane Connection? I would say no. If you have an Arcane Connection to something, in general you cannot just "make magic happen in its vicinity" (of course there are individual exceptions, e.g. if you have an Arcane Connection to a Structure, you can target all its contents).
Did I misunderstand you? Everytime I re-read this, what I understand is Pilum of Fire at arcane connection range is impossible without a Wizard's Tunnel. Also, yes, I would say you could create a cat at arcane connection range. It would make more sense to create a cat at a location at arcane connection range, but I think it could be created on a person (with all the usual caveat about Magic Resistance). Maybe not in the vincinity of a person, but on his lap if he's sitting looks fair to me. For bonus points, add a Rego requisite to make the cat temporarily disposed positively or negatively towards the person.
Oh my, that gives me an idea for a spell that lets you create a black cat on a person you have an AC to, and use it repeatedly to make them seem like a witch/warlock. Especially if all the cats are identical, and are all friendly towards the person.
By how I read the rules, yes, it is impossible in general.
Because Pilum creates a fire, rather than making a target directly hotter.
It comes from the Limit of Arcane Connections. You cannot affect an unsensed Target without an Arcane Connection to it (in this case, the Target is the fire).
Note that this is different from "you cannot affect an unsensed Target without an Arcane Connection to something close". If you hold someone's left hand, and that someone is 100 miles away, you can affect him, or his right hand if it's still attached to his body, because it's as if his left arm were mystically 100 miles long and stretched all the way to you. But you cannot in general affect the tree he is touching with his right hand.
Think about it. Suppose you are touching the base of a very tall tree. Can you create a bird on its furthest branch at R:Touch? Not unless you can reach there.
You made me doubt here for a moment. The thing is that it is a general property of creo spells of being unsensed prior to creation. By that logic, a cat could never be created, because you could never sensed it before casting your spell (nor would you be able to find an arcane connection to something that is inexistant, as you pointed out). And yet Creo spells work.
The limit of arcane connection is not a limit for your spells at arcane connection range. It's a limit for your spells cast blindly, which arcane connection can override. The actual exemple is casting a Perdo Corpus spell to kill everyone in a room you don't see in. It doesn't work until 1) you scry, or 2) you have an arcane connection to your unsensed target on the other side of the wall. The AC lifts the prohibition, rather than being the object of the prohibition.
As for vincinity effect for creo spells at AC range, I went to dig and found Trigger the Distant Power, a Creo Imaginem at arcane connection range, which makes a sound in the vincinity of its AC target. I'm sure there are other such effects.
Well, I feel I am a bit on a shaky ground too
But I am much more convinced of my side of the argument for now.
The point is that if you create a fire at e.g. R:Sight or R:Touch, you sense it as you create it. You wouldn't - in general - sense a fire created at R:Arc.
It lifts the prohibition, but only for the connected object - which you can "mystically touch" because you have a piece of it. It does not act as a positional "beacon".
It's like having grabbed the 100-mile-long tail of some strange beast: you can then easily affect the whole beast despite not having the faintest clue about its position, but not what's in its paws - including creating something in its paws.
I'm not terribly fond of MoH as a source. I find it often violates other rules, written or unwritten. For example, Trigger the Distant Power has absolutely no modifier for versatility and still allows you to produce any sound -- while ArM5 and other books show clearly that Created illusions must be at least a little specific (e.g. a fire, an animal, a person).
And I would be a little more convinced if you could come up with a Form other than Imaginem, Mentem or Vim. That's because it's always tricky to be clear with those "intangible" Forms about what's happening and where. E.g. I would not object to a CrIm spell that, at R:Arc, makes a target appear to burp loudly. Or a CrMe spell that, at R:Arc, makes the target imagine he burped loudly.