Is China at the golden savings rate s? If so, what is it?
To partially answer this question, in Advanced Macroeconomics by Romer, question 1.5(c) asks 


  "What saving rate is needed to yield the golden-rule capital stock?"


Answering this tells us what $s_{gold}$ is.

But before we can find this we must find the golden rule level of capital stock $(k_{gold})$.  Which we shall derive with the following equations: The intensive form of the production function, the dynamics of capital in the Solow Model, and consumption per unit of effective labour

\begin{cases}
Y_t = (A_t L_t)^{1-\alpha} K_t^{\alpha} = A_t L_t \left( \frac{K_t}{A_t L_t} \right)^{\alpha} = A L k^{\alpha} \\
\Rightarrow Y/AL = y = k^{\alpha} \\
\dot{k} = s y - (n+g+\delta) k \\
c = (1-s)y \\
\end{cases}

Under the balanced growth path, $\dot{k}=0$ so 

$$ \displaystyle s k^{* \alpha} = (n+g+\delta)k^* \Rightarrow k^* = \left( \frac{n+g+\delta}{s} \right)^{\frac{1}{\alpha-1}} $$

We maximize $c^*$ with respect to $k^*$ to implicitly define the golden-rule level of capital per unit of effective labour

$$ \displaystyle \frac{\partial }{\partial k^*} c^* = \frac{\partial }{\partial k^*} (1-s)k^{* \alpha} = (1-s)(\alpha k^{* \alpha - 1}) $$

$$ \displaystyle = \alpha (1 - s) \left( \frac{n+g+\delta}{s} \right)^{\frac{\alpha-1}{\alpha-1}} $$

Next replace $s$ with $(n+g+\delta)k^{* 1-\alpha}$

$$ \displaystyle = \alpha (1 - (n+g+\delta)k^{* 1-\alpha}) \left( \frac{n+g+\delta}{(n+g+\delta)k^{* 1-\alpha}} \right) $$

$$ \displaystyle  0 = \alpha (k^{* (\alpha-1)} - (n+g-\delta)) \Rightarrow k^*_{gold} = \left( \frac{\alpha}{n+g+\delta} \right)^{1/(1-\alpha)} $$

We can finally compute, $s_{gold}$

$$ \displaystyle s_{gold} = (n+g+\delta) k_{gold}^{*1-\alpha} = (n+g+\delta) \left( \frac{\alpha}{n+g+\delta}\right)^{(1-\alpha)/(1-\alpha)} = \alpha $$

So for a Cobb-Douglas production function the golden-rule saving rate should be whatever $\alpha$ is.