I got my first comment, but unfortunately it is rather scathing. Obviously, I missed my goal, possibly even achieving an effect contrary to the expected one: obfuscating instead of enlightening :-(
The strange thing though is that researching the subject has unearthed different papers that essentially use the approach I want to follow. I guess this is not the approach per se that is wrong, but my own take on it. I'll try to realign my presentation towards a more concise and elegant approach as suggested by the anonymous scholar.
On a side note, comments are always welcome, even negative ones. You cannot get better if you don't know your bad points. Constructive criticism is obviously preferable to a blanket repudiation, but I'm afraid I'm not the one calling the shots. But in some other ways, a blog can be seen as a form of mental masturbation, so I'll continue even if I fail in my stated goal, I can still enjoy the act of writing itself
My (restated) goal is to construct a simple mathematical expression that calculates the tax owed in function of all necessary parameters. I found in "Effective Federal Individual Income Tax Functions: an Explanatory Empirical Analysis" a citation that summarizes the approach I want to follow in a concise way: "... a tax law is a mapping from a vector whose elements are the income characteristics of the individual (wage income, dividends, capital gains, and all the other items in the income tax form) to tax liabilities. It is supposed to be a well defined function; ..." taken from Arrow, Kenneth J. "Microdata Simulation: Current Status, Problems, Prospects." in Microeconomic Simulation Models for Policy Analysis, New York: Academic Press, 1980.
I want to construct this mapping. This mapping is simple in the sense that it only uses elementary operations, the final form is piecewise linear and mostly continuous, this sounds simple to me and I want to expose this simplicity for everybody to see