= Oriented connector crossing count
{title2=$dN/dS=n|\mathbf R\cdot\mathbf n|\psi\,d^3R$}
For a locally uniform distribution of labelled connectors, a connector crosses a small surface when its midpoint lies in a slab of thickness $|\mathbf R\cdot\mathbf n|$. This gives the displayed unsigned count per unit area. Omitting the absolute value gives a signed count, or requires a restriction to one orientation. The signed spring <force> transmitted from the positive side to the negative side is $H\mathbf R\operatorname{sgn}(\mathbf R\cdot\mathbf n)$, so multiplication by the unsigned count yields <traction> $nH\langle\mathbf R\mathbf R^T\rangle\mathbf n$. Each labelled dumbbell is counted once.
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