Quite the theory constructed out of second hand astronomical knowledge. How again can you know with any certainty what powers the sun except for models that fit the data, rather than the truth?
All we ever have are models. There's never any access to the "truth". This is true for both second hand and first hand knowledge. We are just more aware of some of those models than others. When a little child plays catch with a ball they are using mental models about the movement of balls. When you cross the street at a crosswalk you are using a model that says it is safer to cross there than in the middle of the road. These are all models. The only difference is the degree that the knowledge is indirect. Note that having a lot of indirect evidence doesn't mean that that evidence can't be very strong. All my evidence that George Washington existed is indirect and very second hand. But that doesn't substantially alter my confidence that he existed.
Ok ill try to use simple observations to prove that the sun could not be using fusion if it were only 32 miles in diameter. Objects like jupiter and venus are far larger than 32 miles in diameter, and they have no where near the amount of gravity or density needed to begin fusion. Its at around 13 jupiter masses when we begin to see small amounts of fusion in the core of these large planets, and thats why we begin to call them brown dwarfs.
Also the sun converts millions of tons, perhaps even billions depending on your source, of hydrogen a second in order to produce sufficient amounts of energy to power the amount of pressure that it needs to exert back on gravity to prevent itself from collapsing. Models for the sun are extremely difficult to create, in fact there are entire upper-division classes here at UCSC devoted to constructing models of the sun. If you put in too much mass, it has too much gravity, and will collapse. If you change the density, you change the amount of pressure driving fusion, and therefore change the amount of pressure pushing against gravity, and will cause the sun to collapse. The sun is always in a very close balance between collapsing or expanding rapidly, And this is arbitrary of whether the earth is round or not. You can run the computer models yourself.
Keep in mind also, that its pretty easy to see first hand that nuclear fusion takes immense amounts of pressure and heat to start. One of the few ways, and the most common way that we are able to start fusion reactions, is through the use of fission nuclear bombs.
Now sure, none of this is proof that a 32 mile diameter sun could not (even though the pressures in the center of the earth would be greater than something merely 32 miles across, and therefore would start a nuclear fusion reaction) start a fusion reaction and sustain it for billions of years. But it just doesn't seem to be the simplest explanation to assume that sun is 32 miles across and performing nuclear fusion when there are other objects of greater size that cannot preform the same action, for example, the earth.
But even more important, is the fact that you have not proven that nuclear fusion could actually happen only 3000 miles away from our surface in a body only 32 miles across. If you want, i can give you many links on how fusion in the sun works given the suns size and mass in RE terms. I dont think that you can provide me anywhere near the same level of evidence that this is in fact possible.