I'd like to discuss some of Sophia's math while also proposing balance changes to Sophia.

Probably the most interesting of Sophia's ability is the rebate on Great People purchases, and it is here I'd like to talk math.

Sophia's 40% rebate makes Sophia a monster Great People purchasing civilization, especially if Sophia either finished rationalism or acquired Glory of God as her reformation belief. While this isn't as great as a flat 40% discount as the player is required to pay in full to actually get the GP, it still is a 40% effective discount for every Great People of the same type before the last one.

Great People faith cost in standard speed is calculated like this:
Cn = Cn-1 + 500*n-1, while C1 = 1000 where n means the frequency of the faith purchase of the said Great Person type.

So,
C1 = 1000
C2 = 1500 (1000 + 500)
C3 = 2500 (1500 + 1000)
C4 = 4000 (2500 + 1500)
C5 = 6000 (4000 + 2000)
C6 = 8500 (6000 + 2500)
C7 = 11500 (8500 + 3000)
C8 = 15000 (11500 + 3500)
etc.

If a regular civilization wanted to purchase 5 Great Scientists, it would have to have 15000 faith, which is pretty difficult figure to achieve.

Sophia on the other hand is a bit different. If Sophia wanted to purchase them all at once, Sophia would first purchase the first 4 Great Scientists at effectively 60% of the cost, meaning Sophia would require 11400 faith to purchase all 5 GSs at once, which may seem a bit difficult but with her bonuses to faith it is something Sophia can, but not reliably achieve. (however, such figure can be achieved much more easily with other mods such as Civilization 4 Traits and several Great People oriented mod wonders)

Sophia's true faith game comes into play if Sophia chooses not to buy them all at once, but buy one at a time, use them, then purchase another. Because stacking 5-digit faith is pretty much impossible in the Industrial Era because of the Prophets draining all the faith pool until the Industrial Era while also being unlikely in the Modern Era as well, I am going to assume that Sophia is in the Atomic Era. Then the math becomes deceptively powerful. Sophia receives 100*Era faith (in standard speed) every time she expends a Great Person: what this means is Sophia also gains 700 faith every time she expends a Great Person in the Atomic Era. This further cuts down on the amount of faith Sophia needs to have in the first place: Instead of 11400 faith if Sophia chooses to purchase them all at once, Sophia would only need 8600 faith to be able to purchase 5 Great Scientists with faith, which is perfectly feasible with Sophia since all the other Great People expended after the Industrial Era will also go to fuel Sophia's faith pool.

1st Scientist: -100 net faith cost (600 base, 700 gained from expenditure)
2nd Scientist: 200 net faith cost (900 base, 700 gained from expenditure)
3rd Scientist: 800 net faith cost
4th Scientist: 1700 net faith cost
5th Scientist: 6000 required to purchase

However, all of these bonuses are only available after the Industrial era, and frankly it is only OMGBBQWTF level of awesome at the late Modern Era or later when Sophia has built up the faith pool to spend, so I do not find this part of the bonus to be broken.

The Desert Oracle has become a hot potato, and it is definitely also a deceptively powerful building that is much more impactful than the trait itself that synergizes hilariously well with Sophia's unique improvement.

Special thanks to Caulder who shared his experience, who has stated that it is easy for Sophia to have core cities that yield around 60 faith just before the Renaissance Era.

While it is easy for Sophia to make a supercity churning out crazy tons of faith, I am of the opinion that making more than 1 is much more difficult to do so. Whereas the Dragonstone Monument will ensure that most other cities will generate a good sum of faith (around 10~30 depending on terrain and resource positions), one of the best ways of boosting faith, namely through Holy Sites, is quite difficult to do. In my test game where I've used Civ IV Traits and Wonders (from which I managed to build some core wonders) which significantly helped Sophia, I've only managed to plop down 6 Holy Sites, and that's after picking up Messiah as the faith. Nevertheless, I'd like to talk about both the main city which will be the core source of faith, as well as the peripheral cities which will also generate some faith. By the end of my test game (which as stated before is much more favorable to Sophia than in the vanilla), my capital generated 285 faith, of which 176 came from the effect of a wonder (Asklepieion en tei Koi) and the Divine Inspiration belief (108 and 68 respectively), while my core non-capitals generated around 30 faith, and my fringe cities 18. However, given the nature of how the faith is gained, it can be assumed that most of the faith gains will be made not long after the city is founded and grown to a usable size.

As a point of reference, in my test game I finished the Desert Oracle in my capital at Turn 89 (mainly because I wanted to do a special build), I managed to hit 6 food at turn 102, around 12 turns after the Desert Oracle was built.

I am inclined to slow and as Caulder suggested, significantly lower the cap on the Desert Oracle Food bonus. However, I am of the opinion that the food threshold should be raised to slow down the food growth, as the Desert Oracle can definitely help feed cities: Even in core cities which generate 30 faith, It'd take 21 turns (probably more as the faith still needs to be built up) to hit 6 food, which is basically Hanging Garden bonus. Instead of 30, The base set to something like 48 so instead of 30-60-90 etc, 48-96-144-192 etc.

Probably the most hidden of Sophia's bonuses, the Dragonstone Monument yields great benefits to Sophia's economy. It is most similar to Gangrel's Grima Shrine, so I will primarily compare this to Gangrel's improvement

Nevertheless, Sophia's improvement yields science instead of Gold, meaning while Sophia won't get a bonus on buying or maintaining armies unlike Gangrel, Sophia can get a tech advantage. However, Gangrel has the advantage of building his improvement sooner: Gangrel's shrine requires Masonry, while Sophia's monument requires Philosophy which is much more difficult and slower to get to.

Gangrel's improvement has following advantages over Sophia's

• Requires only Masonry
  
• Yields 2 Food at Engineering (Sophia requires Education to hit 2 food)
  
• Yields 2 Faith at Theology (Sophia requires Education to hit 2 faith)
  
• Higher total yield at full tech (+2 Food, 2 Faith, and 3 Gold, while Sophia's monument is +2 Food, Science and Faith)
  
• Helps buy and maintain armies
  
• Can be built adjacent to each other

On the other hand, Sophia has the following advantages over Gangrel.

• Builds faster (Build cost 500 vs 700, but since the first build applies twice the build rate, Sophia's monument takes 4 turns while Gangrel's require 6 turns. With Citizenship, Sophia's monument requires 3 turns while Gangrel's shrine requires 5 turns)
  
• Yields Science
  
• Can be built on resources that are not on the Desert, and receive peripheral bonuses not built into the improvement (e.g. Pasture/Plantation/Camp bonuses)

Because Sophia's improvement build so fast and can develop any resources, Sophia has a great advantage in utilizing seemingly poor luxury starts: Camp and plantation resources are often frowned upon because luxury Plantations and Camps only give gold as its bonus until fertilizers. Sophia on the other hand can simply first develop the resource, then later hit Philosophy and quickly build a Dragonstone Monument to make such resources much more useful. Furthermore, because Sophia's improvement can be used to make already desirable tiles even more desirable to work, Sophia can also be a surprisingly good wide civilization. Whereas Sophia can transform a sheep (hill) tile into a 3 food 2 production 1 faith 1 science tile, Gangrel cannot, and wide civilizations work best when working choice tiles that provide maximum benefits. While Gangrel can work better on a stretch of desert than Sophia as he can spam the Grimleal shrine in a way that Sophia cannot, flat deserts are usually not good places to expand, and Gangrel's inability to build these things on resources make it surprisingly difficult for Gangrel to take advantage of pesky resources lying in the desert (especially those yucky Desert Incenses!). However, Gangrel's ability to spam 2 Food improvements in all resourceless desert tiles with a lower tech investment will mean Gangrel will get ahead, particularly on Gold which he can use to raise an army. So whereas Gangrel will fare better at the desert and gets bonuses much earlier, Sophia makes up for it with terrain flexibility and science.

However, because the improvement yields faith, this synergizes with the Desert Oracle (as described in the above section), allowing Sophia to maintain large cities as long as Sophia has the happiness to maintain them.

Tl;dr: Dragonstone Monument is great, the Trait is cool but not particularly gamebreaking but the main balance breaker is Desert Oracle's food bonus