Offer a mechanistic explanation for each of the following reactions:
a. The 3,5 -dinitrobenzoate esters of the stereoisomeric bicyclo[2.1.0]pentan-2-ols shown below both yield cyclopent-3-enol on hydrolysis in dioxane-water. The relative rates, however, differ by a factor of 10 million! Which is more reactive and why?
b. Optically active 4-A racemizes on heating at $50^{\circ} \mathrm{C}$ with a half-life of $24 \mathrm{~h}$.
c. On being heated to $320^{\circ}-340^{\circ} \mathrm{C}$, compound 4-B produces $1,4-$ dimethoxynaphthalene and 1-acetoxybutadiene. Furthermore, deuterium labeling has shown that the reaction is stereospecific as indicated.
d. It has been found that compounds 4-C and 4-D are opened at $-25^{\circ} \mathrm{C}$ to allylic anions in the presence of strong bases such as lithium $t$-butylamide. In contrast,
e. When the 1,6 -methano- $1,3,5,7,9$-pentaene structure is modified by fusion of two benzene rings as shown in 4-Fa, a valence isomer 4-Fb is the dominant structure.