## Future Research and General Thoughts

The obvious next step in pursuing the MDM model is to consider relativistic effects; that is, to construct a quantum field theory with a complex value of the discretization index. At present, QCI is a non-relativistic formulation. QFT could allow us to consider how QCI might affect cosmology and the early universe, or the behavior of particles moving at relativistic speeds. As such, the construction of a relativistic version of QCI / MDM is the current goal of our research.

We have also given some thought to making the formulation mathematically rigorous. The Appendix of our paper considers some early work in this regard. The fundamental issue is the computation of multiple integrals with a complex number of variables, as well as sums with a complex number of terms. We might follow a similar procedure as the construction of "pseudo-functions", like the Dirac Delta function, which are not strictly defined as functions, but which possess well-defined integrals.

We also might consider using other norms besides the p-norm. This could significantly extend spectrum of possible universes. A use of quaternions, rather than complex numbers, might also generalize these results. In the end, we would be interested in an anthropic multiverse calculation, determining the likely index phase corresponding to our universe. Such a determination could allow us to pursue experimental verification. For example, if our universe's index phase is small but non-zero, astronomical observations, if detecting a gradual fall in star luminosity over billions of years, would offer strong evidence of QCI.

We have also given some thought to making the formulation mathematically rigorous. The Appendix of our paper considers some early work in this regard. The fundamental issue is the computation of multiple integrals with a complex number of variables, as well as sums with a complex number of terms. We might follow a similar procedure as the construction of "pseudo-functions", like the Dirac Delta function, which are not strictly defined as functions, but which possess well-defined integrals.

We also might consider using other norms besides the p-norm. This could significantly extend spectrum of possible universes. A use of quaternions, rather than complex numbers, might also generalize these results. In the end, we would be interested in an anthropic multiverse calculation, determining the likely index phase corresponding to our universe. Such a determination could allow us to pursue experimental verification. For example, if our universe's index phase is small but non-zero, astronomical observations, if detecting a gradual fall in star luminosity over billions of years, would offer strong evidence of QCI.