Mechanism? That sounds like dancing!



No, Ralphie! A mechanism shows the progress of a reaction using arrow-pushing!

This is the mechanism for the rhodium-catalyzed conversion of 5 to 4:



First the α-carbanion (shown in resonance) attacks the rhodium(II) acetate.

This catalyzes the leaving of the diazo group as free nitrogen.

Next the OH group can attack the α-carbon, which frees the rhodium-acetate.

Once the carbanion is protonated, ta da! You've afforded molecule 4!

Up next, the experimental!



Citations
Gong, J.; Lin, G.; Sun, W.; Li, C.-C.; Yang, Z. J. Am. Chem. Soc. 2010, 132, 16745–16746.
Dorwald, F. Metal Carbenes in Organic Synthesis; Wiley: Weinheim, 1999.
Doyle, M. P., McKervey, M. A.; Ye, T. Modern Catalytic Methods for Organic Synthesis with Diazo Compounds; Wiley: 1998.
Qu, Z.; Shi, W.; Wang, J. J. Org. Chem. 2004, 69, 217–219.