The new mirror matter theory has only a very rough framework with many of its aspects waiting to be greatly improved and further developed as a nascent research direction. In particular, its mathematical rigor and foundations have yet to be established. Relevant new mathematical tools and approaches are desired to be implemented in the new theory. Theoretical efforts in the past several decades on fundamental physics, especially on topological quantum field theory, string theory, and quantum gravity, need to be merged into the new theoretical framework under the guidance of the newly proposed first principles. Most importantly, the neutral hadron oscillation effects predicted by the new theory are ready to be experimentally tested in laboratory, and it is time for more observation and simulation works in astronomy and cosmology under the consideration of the new theory to be conducted.
As presented below, I’d like to say a few words on the future direction of the new theory to interested mathematicians and physicists.
