F-Structure
   α ≈  0.00729735256808165960645673176449504568553711123018784582341251360120766198943180839353433540695703116593287
1/α ≈  137.035999106574850947033487500102527970645630197858252856934296915428179524442063181589178337611066258136613

As of 2018-05-14 and 2023-10-13, the Fine Structure is now a defined constant

Why is The Fine Structure Constant of dimension 1?
It's because, like π , it is a ratio, of two like units!

The Fine Structure Constant α is a measure of the interactions between light and charged elementary particles such as electrons. [1]

In 1928 Charles Janet published his left-step periodic table of chemical elements. He believed that no elements heavier than 120 would be found. [2]

What does this equation tell us about the meaning of the Fine Structure Constant? Arnold Sommerfeld introduced the concept of the fine structure constant in 1916, during his extension of the Bohr model of the atom to include the relativistic relationship between mass and velocity and elliptical orbits. [3]

Concerning the nucleus, Sommerfeld tried to connect the number 8 and the number of corners of a cube. [4]

Gluons that mediate the strong interaction between quarks only come in eight varieties. The number 8 figures prominently throughout this equation. [5]

Concerning the electron field, we have only four shells. The maximum number of electrons that can occupy shells one through four are, in sequence, 2, 8, 18, 32. [6]

For each of the four principal energy levels, the total possible occupying electrons that can fit in any given shell is 2n2. [7]

The Stowe Table of Elements shows this 2 8 18 32 sequence in visual form from 1s to 8s. There are eight principal quantum numbers. This seems to relate to the 'octet rule' where elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. In general, the rule is applicable for the s-block and p-block.
There is an analogous 18-electron rule for transition metals. [8]

In the Complete List of Orbitals, there are only sharp(with 1 orbital), principal(with 3 orbitals), diffuse(with 5 orbitals), and fundamental(with 7 orbitals). This is the meaning of the fine structure constant, that it is explicitly related to both the nucleus of the atom and the surrounding electron cloud. [9]

This strongly implies that there will never be more than 120 elements. If there were more, then the Fine Structure Constant would have a different value.

[1] National Institute of Standards and Technology
       https://physics.nist.gov
       Fundamental Physical Constants
[2] Wikipedia
       https://en.wikipedia.org/wiki/Charles_Janet
       Charles Janet, Wikipedia (consulted June 7 2024).
[3] Science Notes
       https://sciencenotes.org/fine-structure-constant/
       Fine Structure Constant
[4] Nobel Lectures in Physics
       https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics42-62-1.pdf
      1942-1962
[5] Forbes
       https://www.forbes.com/sites/startswithabang/2020/11/18/why-are-there-only-8-gluons/?sh=13a9edf47ad8
      Why Are There Only 8 Gluons?
[6] Britannica
       https://www.britannica.com/science/shell-atomic-model
      shell atomic model
[7] University of Illinois at Urbana-Champaign
       http://www.chem.uiuc.edu/rogers/text5/Tx53/tx53.html
      An Atomic Model
[8] The INTERNET Database of Periodic Tables
       https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=38
      Stowe's A Physicist's Periodic Table
[9] Florida State University Chemistry and Biochemistry
       https://www.chem.fsu.edu/chemlab/chm1046course/orbitals.html
      Orbitals and Bonds