Ridge-closed connected layer families of rank two have length exactly $n-2$ at most

For rank $d=2$ on $n\ge2$ symbols, a ridge-closed layer is a clique on its active symbols (a pair whose two singletons are active must be present). The maximum length of a ridge-closed connected layer family of rank two is exactly $n-2$: the bound because consecutive cliques must be edge-disjoint and each symbol's activity is an interval, so each transition retires or introduces a symbol; attained by the sliding pairs $\{t,t+1\}$. This is far below the unrestricted rank-two optima (which reach $2n-\log_2 n-2$, Hirsch.clf_rank_two_doubling_family), showing that ridge-closure genuinely shortens families at fixed rank even though it is exponent-preserving across ranks.