I understand that the sliders "influence" the number of hammers per colony. BUt what is the base variable PER planet that the "hammers" are calculated from???
The question that you're asking is what can you do to get more social production-and the answer is to build more factories. The math for the actual social production (and, incidentally, military production, although research is slightly different) is outlined below.
The "base variable" per planet is not the same for all planets-nor for all versions. From memory, in DA, it's 16 for a colony, and 24 for your HW, whereas in TA it's 14 for a colony and 24 for your HW.
However, to this you must also add any factory improvements you have built on the planet in question-if I add a Manufacturing Center to a Colony in DA I now have 24 (14 colony + 10 MC). Additionally, this is the point that any bonuses from asteroid mines are added in (if I remember correctly-it's possible they don't get racial bonuses, but I've forgotten that).
Finally, you take your base value above and multiply it firstly by funding-let's say our 24 social times 50% funding for 12 social-and then by any relevant racial modifiers. "Racial modifiers" include anything you get from technologies-like Xeno Engineering-any bonuses to social production on a planetary basis such as a moon or an event, and last but not least any economic starbases that have the planet in its area of effect (for almost all intents and purposes the maximum is 24 SBs, but as it's virtually impossible for a planet to spawn in such a location, your best bet is 16 maximum). It also includes, of course, anything from customization points or political parties.
All of these values are treated equally, and I refer to all of them as racial modifiers. There also happens to be any bonus you may have from power plants and/or the manufacturing capital, but to be perfectly honest I don't remember where they come in-I suspect it's before the funding.
So with a bonus of 30% social from techs (in DA), and 20% from Industrialist political party (for instance), our above colony with an MC where empire-wide social funding is 50% will generate (14+10)*0.5*1.5=18 social production, without using any focus buttons.
Hope that helps. Research is more complicated. 
