Short Opinion: Extending General Relativity to N-dimensions is not even wrong leading to inventor's paradox

It is original to have a solution to the generic case, so-called arbitrary N in mathematics, such as the N-dimensional case. This is considered as a generic solution in computer science as well, inventor's paradox.

Bohr and Einstein 1925 (Wikipedia)

However, such generalisation to higher-order objects may not be needed for reality. Mathematical beauty does not bring reality with it by default. An example is trying to generalise General Relativity [1]. I think this is a novel work in mathematics but it may not reflect our physical world as it is. This opinion is not new and probably the reason why many decades, community resisted against the attempts to lower the status of General Relativity as a special case of something higher dimensional object [2] that can not be tested. Einstein's theory of GR is good enough to explain our universe and supported with observations [3].

Trying to the extent any physical theory to higher dimensions may not be even wrong if it can not be observed.

[1]  A Generalization of Gravity, arXiv:1409.6757 
[2] Huggett, Nick and Vistarini, Tiziana (2014) Deriving General Relativity From String Theory.
[3]  On Experimental Tests of the General Theory of Relativity, American Journal of Physics 28, 340 (1960); https://doi.org/10.1119/1.1935800

PS: Links added on 13 April 2020