  We give a new proof of the discretized ring theorem for sets of real numbers.
As a special case, we show that if $A\subset\mathbb{R}$ is a
$(\delta,1/2)_1$-set in the sense of Katz and Tao, then either $A+A$ or $A.A$
must have measure at least $|A|^{1-\frac{1}{68}}$
