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I am looking for some guidance assigning the $J$ coupling constants to the corresponding hydrogens. Here is my data:
I can obviously see that shift 3.56 is for the methyl group. I can also see that the 4.63 is for the hydrogen adjacent to the methoxy group as it can only couple ($J=\pu{0.8Hz}$) to one hydrogen next to it. Is the approach then to see that the hydrogen at shift 4.04 also has $J=\pu{0.8Hz}$ so this must be adjacent (going clockwise from C of methoxy, next C along)?
Coupling constants are mutual. If nuclei $\ce{A}$ and $\ce{B}$ couple and this coupling results in a coupling constant $J_\ce{AB} = \pu{7.4Hz}$ on $\ce{A}$ then $\ce{B}$ will also be split into two signals with a coupling constant $J_\ce{BA} = \pu{7.4Hz}$.
Therefore, you can indeed start at the anomeric hydrogen (which you can identify not only by the coupling pattern but also by its chemical shift) and work your way along the ring, noting whether two hydrogens are in gauche or anti configuration along the way.
