= Smooth-curvature high-force extension law
{title2=$\langle\mathcal L-L\rangle/L\sim B^2\langle(\kappa_0')^2\rangle/(2F^2)$}
For a stationary <quenched intrinsic curvature> with <power spectrum> $S_\kappa(q)$ and finite second spectral moment, the bulk deficit satisfies
$$
\frac{\langle\mathcal L-L\rangle}{L}=\frac{B^2}2\int\frac{dq}{2\pi}\frac{q^2S_\kappa(q)}{(F+Bq^2)^2}
\sim\frac{B^2}{2F^2}\int\frac{dq}{2\pi}q^2S_\kappa(q).
$$
The moment is $\langle(\kappa_0')^2\rangle$ for mean-square differentiable curvature. Infinite-moment disorder and finite endpoint boundary layers can change the exponent, so this is a smooth bulk law rather than a universal law for all random polymers.
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