rely even on Einstein equations. This method can in principle directly measure the space-time curvature but cannot test a modification of gravity. On background level, the power of observations to constrain the expansion history of the universe by assuming $\Lambda$-cold dark matter ($\Lambda$CDM) as a null test was studied in Refs [@Shafieloo:2009hi; @Shafieloo:2011zv], while a principle-component analysis of the equation of state constraints was developed in Ref. [@Huterer:2002hy]. Recently, even the validity of the assumption of the Copernican principle was tested [@Valkenburg:2012td]. On the level of linear perturbations, parameterizations are usually used to limit the freedom in the model-independent description of growth of structure [@Caldwell:2005ai; @Linder:2005in; @Hu:2007pj; @Amendola:2007rr; @Bean:2010zq], although principle components analysis has also been employed [@Pogosian:2010tj]. Another way to limit the freedom in the fully general description is to exploit the structure which any general-relativity-like theory of dark energy must obey: such approaches were discussed in [@Bertschinger:2006aw; @Baker:2011jy; @Battye:2012eu; @Baker:2012zs]. All of the above approaches, when contrasted with data, require parameterizations in order to break degeneracies, but simultaneously introduce parameterization-dependent biases.

The difference of our approach is that, given the minimum of assumptions, we *first* elucidate the observables that measurements can in principle provide without the assumption of 