"rigorously demonstrated" is a correct and usable phrase in written English.
You can use it when you want to emphasize how thorough or extensive a demonstration has been. For example, "The efficacy of the proposed treatment for the illness was rigorously demonstrated in the study."
While investigators rigorously demonstrated the disinformation, some consumers of these conflicting narratives will inevitably be skeptical as to who did what.
Later, with R.J. DiPerna, Lions rigorously demonstrated the existence of solutions to Boltzmann's equation for the density of colliding hard spheres, given general initial data.
First Cantor rigorously demonstrated that the set of rational numbers (fractions) is the same size as the counting numbers; hence, they are called countable, or denumerable.
Although doctors assume that the treatments are more or less equivalent to prostate surgery, that has not been rigorously demonstrated, nor has it been shown that these treatments prevent prostate cancer deaths.
Many potential strategies for CSC-directed thavepy have been proposed, but few studies have rigorously demonstrated their efficacy using in vivo models.
This is the kind of claim you'd never get away with in a scientific paper, not unless you rigorously demonstrated your method was truly better than everything else.
This work rigorously demonstrates the accuracy and limitations of the standard model through analytical derivation and comparison with an efficient numerical solution.
In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately.
Further, studies for heterologous expression, purification, and biochemical characterization of other genes are currently underway to rigorously demonstrate involvement of both the pathways.
The second additional criticism is that Alexander's documentation also fails to rigorously demonstrate the fundamental premise that beautiful environments are comprised of greater numbers of patterns than the contemporary designs which are allegedly destroying the world [9].
For example, it took us several years and multiple knockout lines to rigorously demonstrate that PAP, NT5E and TNAP act redundantly to generate adenosine from AMP.
