So, I've been toying around with Ars Notoria, trying to figure out how it works, and frankly, I don't see how you did it. You glossed over the numbers for reciting the rings, so I can't check them. But I really don't see how you got to the ease factors for reciting the rings.
You have a base of Int + Ars Notoria + Modifiers for reciting a ring. At the start, you have the following numbers:
Int: 2
Ars Notoria (as of first recitation: 5
Modifier for Optimistic: +3
Modifier or Compassionate: +1
TOTAL: 11
The EF for reciting a ring for the first time is 6 + 3*ring + 1/season.
We'll assume all first recitations are for a single season to keep the EF as low as possible.
The EF for reciting first ring = 6 + 3*1 + 1 = 10.
You have a +11, so you should be okay (unless you botch; you really ought to post die rolls where you can botch).
The EF for reciting second ring = 6 + 3*2 + 1 = 13.
You have a +11, so you should be okay (unless you roll a 0 or a 1).
The second ring also ups your Int to +5 when in effect. We'll assume you manage to keep it in effect for all future recitations. That ups your total modifier to +14.
The EF for reciting third ring = 6 + 3*3 + 1 = 16.
You have a +14, so you should be okay (unless you roll a 0, 1 or 2).
So far so good. You've rolled well and managed each ring on the first try.
At this point your Ars Notoria goes up to 6, which raises your total modifier to +15.
The EF for reciting fourth ring = 6 + 3*4 + 1 = 19.
You have a +16 (+1 for specialization), and it's starting to get tricky. You need to roll a 4-9 on the die, which is only a 60% chance.
The EF for reciting fifth ring = 6 + 3*5 + 1 = 22.
You have a +15, and it's really chancy now. You need to roll an 8 or 9 on the die. It seems like you'd have to try a lot to get this to work.
At this point, your Ars Notoria rockets up to 9. That makes your total modifier +18
The EF for reciting sixth ring = 6 + 3*6 + 1 = 25.
You have a +18, and it's still really chancy. You need to roll an 7-9 on the die. It seems like you'd spend more than one season trying this.
The EF for reciting seventh ring = 6 + 3*7 + 1 = 28.
You have a +19 (specialization in 7th ring), and now you need to roll a 9 on the die. That's a 1 in 10 chance, with the possibility of a botch on each roll.
Now, perhaps you were fasting (I saw no indication of that, nor no rolls), or you were chaste (again no indication and no rolls), but I can't be sure.
All of this also assumes that Poenitens never committed so much as a venial sin during all this time, which is really quite impressive. (Though I'll admit that there's no way to easily track sin during pre-game times.)
Am I missing something? Are there some bonuses I haven't accounted for? Because right now it seems like the chances of success on all seven ring on the first try would be vanishingly small.