Theorem:
In a group of 5 Atoms in a single Domain, where no Atom shares the same exact Essential Letters as another Atom, then there must be at least one bonded set of Atoms.
(Or formally: FE ( {A},{B},{C},{D},{E}, P(A,“essential letters”) <> P(B) ... ) -> {A}::{B} or {A}::{C} or {A}::{D} ... = 1 )
Pretty simple theorem and easy to prove, but up for grabs.
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Arlnoff:
1. For a group of unique Atoms to have no bonds between them, they must all have one Essential Letter in common.
2. There are exactly four unique Atoms which all share one Essential Letter, because there are only five Essential Letters and one Atom cannot have the same Essential Letter twice. (Example: HK, HR, HY, HW)
3. Therefore, any attempt to add a fifth unique Atom into the group necessitates it not having the Essential Letter which the previous four shared.