Right, I understand how the lux slider works.
But there has to be a specific formula or set amount of gold that will make citizens content or happy.
My question is specifically for the very early game, so I am assuming that war or luxeries or foreign citizens are not part of the equation.
The reason I want to know this is so I can project how much research my capital and/or core cities will be able to produce, about 50 turns into the game. In order to know that, I need to know specifically how I would use the lux slider.
This may not fully answer your question...However, a good rule of thumb is each 1 commerce point = 1 empire-wide gpt OR = 1 beaker OR 1

.
That means each

takes 1 commerce point per turn to produce (unless the

is due to city improvements, MPs, luxes, etc). I think it's progressive, in that it takes 1 commerce point for 1 unhappy citizen for 1 turn to move to content, and it takes 1 commerce point for 1 content citizen for 1 turn to move to happy.
I'm emphasizing the "each turn" nature of this because, obviously, how your commerce points are distributed can change each turn depending on the happy slider, city size, etc.
The best thing I can tell you is to look inside a city screen at the bottom-center breakdown of allocations between the treasury, science beakers, and happiness. These allocations reflect the F1 sliders. By playing around with what tiles the city works--which dictates how much commerce per turn that city produces--notice the different allocations across the three categories and see how the happiness of the city can change.
So, this is one more reason why having high commerce in a city is so important, because it strongly influences how many happy

that city has. Often times, a city can be made to not revolt simply by changing its worked tiles to higher-commerce ones.