To pick up from Max Gordon's answerMax Gordon's answer, the zero values of $\beta$ correspond to the unit values of the hazard ratios. Hence a ``strong'' result would be that the hazard ratios are sufficiently far from 1.
However, while hazard ratios are more interpretable than coefficients themselves, inference is weird in that scale, and asymptotic normality of results requires larger (often much larger) samples. To overcome this weirdness, Stata reports an asymmetric confidence interval for the ratios, exponentiating the endpoints of the CI obtained on the scale of coefficients. Thus instead of looking at hazard ratios and their standard errors, I would advise looking at the confidence intervals.
(This has nothing to do with the debate about p-values, null hypothesis testing, Bayes factors, effect sizes, and any of that philosophy. This is just plain higher order asymptotics.)