Plausible universality of uniaxial order in self-assembly of cross junctions in space dimension $d \ge 3$ (opens in new tab)

arXiv:2602.21673v1 Announce Type: new Abstract: We consider the self-assembly of cross junctions in a general space dimension ($d$) as an extension of the problem studied in a previous paper for $d = 3$. This problem is equivalent to constructing a $d$-dimensional hypercubic jungle gym, at all junctions of which $2d$ rods with different colours meet. The analysis reveals a unique feature of the $d = 3$ case: the forced presence of at least one perfectly-ordered (singly coloured) direction (a...