Stable Non-BPS States in F- theory

F-theory on K3 admits non-BPS states that are represented as string junctions extending between 7-branes. We classify the non-BPS states which are guaranteed to be stable on account of charge conservation and the existence of a region of moduli space where the 7-branes supporting the junction can be isolated from the rest of the branes. We find three possibilities; the 7-brane configurations carrying: (i) the D_1 algebra representing a D7-brane near an orientifold O7-plane, whose stable non-BPS state was identified before, (ii) the exotic affine E_1 algebra, whose stable non-BPS state seems to be genuinely non-perturbative, and, (iii) the affine E_2 algebra representing a D7-brane near a pair of O7-planes. As a byproduct of our work we construct explicitly all 7-brane configurations that can be isolated in a K3. These include non-collapsible configurations of affine type.