The curvature coefficient conjecture for the geometric stochastic heat equation

In the setting of the invariant measure conjecture, let $c$ be the universal constant multiplying the scalar-curvature term in the geometric stochastic PDE

$$\d_t u=\Nabla_{\d_xu}\d_xu+\bigl((d A^\flat)(\d_x u)\bigr)^\sharp-\nabla_A A-{1\over 2}\nabla\div A+c\nabla R(u)+\sqrt 2\sigma_i(u)\,\xi_i.$$

Curvature coefficient conjecture. The universal constant is

$$c={1\over 8}.$$

Several values have appeared in path-integral and discretisation approaches, so the conjecture selects the value corresponding to the authors' normalisation; it remains unresolved in the supplied text.