Isolated singularities of solutions to the Yamabe equation in higher dimensions I

We complete, in the Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for $3\le n\le 29$, initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for $n\ge 30$ in our subsequent paper.