A short arithmetic program producing four CODATA-level constants

Questions
,
1

I would like to share a compact deterministic arithmetic program that produces four numerical values lying within the CODATA 2022 one-standard-uncertainty windows for:

  • the inverse fine-structure constant
  • the proton/electron mass ratio
  • the muon/electron mass ratio
  • the tau/electron mass ratio

The code was motivated by a broader physical framework, but the point of this post is not to argue for that framework.

The narrower question is this:

Can this compact computational object be explained as ordinary numerical fitting, and if so, where is the fitted information stored?

The program contains:

  • no empirical target constants as inputs
  • no decimal fit coefficients
  • no continuous optimization loop
  • no output-specific adjustable parameters

In addition, the three mass-ratio outputs share the same denominator ladder.

Wolfram Language code:


        u = 1;
        r = 3;
        A = r*(r - u);
        B = 2;
        n = A + B - u;
        rel = A + B + r;
        ph = n + B;
        h = (rel + u) + n;
        nVal = r + rel + ph + h;
        cVal = 2*nVal;
        atten = 1 - A/n^2;
        Phi = nVal*r + rel + r/cVal + (rel - ph)/cVal^2 + (18/(n*Pi))*atten/cVal^3 + (4*Pi)*atten/cVal^4;
        d1 = r + ph + u;
        d2 = h*(nVal - (r + u));
        d3 = d1*d2;
        d4 = d2*(nVal - (r + u))*A*(rel - r);
        Psi1 = cVal*(h + r) - (ph + r) + (rel - ph)/d1 - u/d2 + (rel - ph)/d3 - u/d4;
        Psi2 = h*rel - r + (rel - u)/d1 - u/d2 + (r + u)/d3 + (h - r - u)/d4;
        Psi3 = nVal*(cVal - u) - ph + (rel - ph)/d1 - (rel - ph)/d2 + (r + u)/d3 - (r*h)/d4;
    
    NumberForm[N[{Phi, Psi1, Psi2, Psi3}, 15], 15]


Output:

    {137.035999165800, 1836.15267343627, 206.768283284455, 3477.15145895483}

For comparison, the CODATA 2022 reference values are approximately:

    alpha^-1          = 137.035999177(21)
    
    proton/electron   = 1836.152673426(32)
    
    muon/electron     = 206.7682827(46)
    
    tau/electron      = 3477.23(23)



All four outputs lie within the corresponding one-standard-uncertainty windows.

Under a conservative unit-range normalization, the four simultaneous window hits roughly correspond to ~66 bits of target-window information.

So my question is simple:

**If this is ordinary numerical fitting, what is the information channel?**

For completeness, I include a short note containing the description-length analysis:

[https://doi.org/10.5281/zenodo.20158423](https://doi.org/10.5281/zenodo.20158423)


  [1]: https://doi.org/10.5281/zenodo.20158423