  We continue to explore, in the context of a toy model, the hypothesis that
the interacting universe we see around us could result from single particle
(undergraduate) quantum mechanics via a novel spontaneous symmetry breaking
(SSB) acting at the level of probability distributions on Hamiltonians (rather
than on states as is familiar from both Ginzburg-Landau superconductivity and
the Higgs mechanism). In an earlier paper [7] we saw qubit structure emerge
spontaneously on $\mathbb{C}^4$ and $\mathbb{C}^8$, and in this work we see
$\mathbb{C}^6$ spontaneously decomposing as $\mathbb{C}^2\otimes \mathbb{C}^3$
and very curiously $\mathbb{C}^5$ (and $\mathbb{C}^7$) splitting off one (one
or three) directions and then factoring. This evidence provides additional
support for the broad hypothesis: Nature will seek out tensor decompositions
where none are present. We consider how this finding may form a basis for the
origins of interaction and ask if it can be related to established foundational
discussions such as string theory.
