People are actually reading and citing my posts! I was in grad school for 3 years and nobody ever read anything I wrote.
The 3 sliders are your "base production". Your base production is determined by planet quality and population. You use your military/social/research slider to decide how your base production is allocated, rounding down. Then, you use your overall spending slider (below your tax bar) to decide what level you're funding. Then, bonuses are added to each individual category.
Your base production is determined by planet quality and population. How much of that base production you can use depends on how much cash you have available. Your sources of cash are taxes, trade, and tribute. Normally, production is "1 for 1". One BC gives you one unit of military, social, or research. Bonuses allow you BOTH to spend more AND to get some "free" production. That's why increasing your bonus causes you to lose money. Your capacity increases, but your income stays the same. The bonus is worth it, because part of the bonus is "free". You can move down your overall spending level. You'll find a point where your net income is the same as before the bonus, but you're producing more.
Suppose you have a "base production" of 100 on a planet. You allocate 50% military, 25% social, 25% research. You are funding at 50%, so your base spending is 25 military, 12 social, 12 research (always round down). Now, add in the bonuses. If you have +20% military and social, with 10% free, your military is 29+5, your social is 13+1, for a total military spending of 29 and a social spending of 13. If you have +100% research, with 50% free, your research is 18+6. Your total spending is 29+13+18, and you're getting 29+13+18+5+1+6 BC worth of production.
Now suppose you went with 100% research, still funding at 50%, with the same bonuses. Your research is 75+25. You're spending 75BC for 100BC worth of research. Notice that you're spending more, even though all you did was reallocate your spending. That's because your base production buys more real production, when you choose to spend on research.
If this wasn't complicated enough, remember that military+social production is capped at 10x planet quality and the military+social bonus is capped at 3x planet quality. Taxes are capped at 4x planet quality. So, you can run into the perverse situation when getting a resource, wonder or social improvement provides no benefit. I consider this to be a design flaw in the game. To be fair, resources, wonders, trade goods, and social projects should increase the cap. Research does not appear to be capped in the way that military and social are capped. The caps exist because people were building 10 starbases in a sector for a ridiculously high bonus. As far as I can tell, this is the only part that was abusable.
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I think I can answer my own (foolish) question 
... Your sliders add up to the total production capacity for all endeavors in your empire. So when you set, say, military production to 50%, you're saying you want half of all production resources spent on military. That's why you're income changes as you move the sliders, because different endeavors (miliary, social, tech) don't all cost the same amount of money. Using half your empire's capacity for reasearch is a lot more expensive than using half of it for military construction.