Mechanism for Nagata Alkylation
This reaction of ortho-alkylation of phenols was first indroduced by Nagata and coworkers in 1979 (Ref.1). Accordingly, for example, reaction of a phenol with a large excess of an aldehyde and a  slight excess of benzeneboronic acid in refluxing benzene (or toluene) in the presence of $\pu{0.1 mol}$ equivalent of propanoic acid (or trichloroacetic acid) gave about 97% of the expected product, a 2-phenyl-4 H-1,3,2-benzodioxaborin, as a crystalline product (Ref.1):



Note that the presence of propanoic acid is critical in the reaction (no propanoic acid, no expected product). The authors have suggested that mechanistically, the reaction would have taken place by coordination of an aldehyde molecule to the boron atom of a probable intermediate I (i.e. a substituted  phenyl benzeneboronate), followed by [3,3]-sigmatropic rearrangement (as indicated in II) to give the product, a substituted benzodioxaborin.  

References:


Wataru Nagata, Kyo Okada, Tsutomu Aoki, “ortho-Specific $\alpha$-Hydroxyalkylation of Phenols  with Aldehydes. An Efficient Synthesis of Saligenol Derivatives,” Synthesis 1979, (5), 365-368 (DOI: 10.1055/s-1979-28683).