Frequency has what dimension?

Physicist say frequency is a one dimensional measurement of three dimensional energy density ion the atom. The they tell me frequency is a wavelength measure of distance, which is not energy, by there definition.

 

OK, this is the definition of frequency. 

Then h introduces the error in collapsing the atomic orbital energy to one dimension. h is energy-second, or mean energy * unit, for one unit of the finite curved number line. Got it.This tells me that when using the number line to measure volume, then frequency introduces a one time error, and plank gives the mean value. I interpret the second to be the tick mark on the optimally curved finite number line. C then is simply a scale factor, taking one unit of the finite number line to some other units.

So, lets call energy the third moment in our system of units, since the atomic orbitals are three dimensional. Then Compton wavelength is a measure of volume.

I am struggling a bit with the most efficient partition of states, as in the number of states an Avogadro set can be in.  There is only one solution in the range of partitions we have discovered, and Avogradro is about three times too high.

In other words, whether its the atom or the ball of gas, the minimum redundancy stacking will not do better than the proton, Avogadro is doing three times better, unless I have an error. But I do not think any quantized system can directly know the third moment of something, only the first or second. For example, consider the power relationship between circumfrence, volume and radius. Convert that to a quantized system, and it will always quantize the unit one. In other words, I do not see a geometry where is can measure Phi^N and Phi^N/3, or some combination of a third root, only Phi^N and Phi^N/2.  Hence my SNR falls as Phi^N/2. I never proved what the volume was, I just used the geometry to note the conditions for upward quantization meet the sphere equation. The packing efficiency could easily be three times what I assumed.

Hence my interest in Vitaly, he will show why three sphere packing scales up and the number packed always stays the same.