Wiki has a general picture of the matrix diagonalization problem

In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This concept of diagonalization is relatively straightforward for operators on finite-dimensional spaces, but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies a class of linear operators that can be modelled by multiplication operators, which are as simple as one can hope to find. In more abstract language, the spectral theorem is a statement about commutative C*-algebras. See also spectral theory for a historical perspective.

The vacuum is literally doing this. The model is not infinite, it is finite of very large order.  That is simply what my macro quantizer is doing, diagonalizing this 200 dimensional power law matrix in steps. Physicists like infinite diagonalization because they do things in the limit as dx,dy approach zero.

 When I look close at the spectral theorem I will find, no doubt, that the matrix diagonalizes because the quants are power law and in sorted order.  But, seriously, the vacuum can do nothing else, there is no infinite measure in free space and the vacuum is limited in dimension like any natural process. If we continuously expand the scale (approach infinity) we will find that the quantization noise exceeds the Shannon separation. When charge is introduced the diagonalization is no longer symmetric, I am sure.

On the quantizer.

I have posted the current testing version of the quantizer on the right of the page. I do things in wave/mass pairs to keep the Compton wavelength and handle by adjacent null ratio problem by letting the large quant degenerate into the small at the end of the loop.

At this point I focus on extracting output per sequence count.  We are still better off using a quantizer designed specifically for the quant rates we use, it allows us to extract intermediate products as they would appear in free space. And, being almost done, and it being a simple procedure, and workable on a spreadsheet; I am headed in the right direction.

The other procedure would to to take one of the standard large matrix diagonalization software products and modifying it. I would do that also, as a double check.

But, it is pretty clear what is going on; its a process of sorting and counting; and a dual rate encoder.