I) I have tagged "root-systems" and "algebraic-groups" in this question because: i) the UNSTATED background context for the question involves the root-system of $E_8$; ii) the integer 14 plays an obvious and important role in the internal structure of this root-system.
II) This question is closely related to Jyrki Lahtonen's comment on this question:
and in particular, to the link which he provided in this comment to an "executive summary" of some past work of his.
III) This question is further developed by the more recent post here:
To complete our project, my team must evaluate the energetics associated with various decompositions of the integer 14, e.g.
In addition, since we are dealing here with biomolecular energetics, it is reasonable to hypothesize that evolution's process of natural selection INITIALLY chose energetics associated with the "simplest" sum "$10+4$" and then only later chose the progressively less simple sums ($6+4+4$, then $5+1+4+4$, then $6+5+1+1$).
This evolutionary hypothesis of course makes the assumption that the sum "$10+4$" IS actually somehow "simpler" in a formal sense than the sum "$6+4+4$".
So, does any FORMAL theory of simplicity actually assert that the four sums above can be ranked in terms of their relative simplicity in the obvious way?
If so, please explain in layman's terms and provide a link as well.
Thank you as always for whatever time you can afford to spend considering this matter.