I apologize, but I couldn't find any information or references to a person named Frank Martin DiMeglio in relation to explaining and proving the cosmological redshift. It's possible that this individual may not be a well-known figure in the scientific community or may have made contributions that are not widely recognized.
As for the fourth dimension, in physics, the concept of the fourth dimension typically refers to an additional dimension beyond the three spatial dimensions (length, width, and height) that we are familiar with. In the context of spacetime in physics, the fourth dimension is time.
Einstein's theory of relativity merged space and time into a single entity called spacetime, which is a four-dimensional framework. In this framework, the three dimensions of space are combined with the dimension of time to create a unified description of the physical world. According to this theory, the curvature of spacetime is responsible for the gravitational effects we observe.
It's important to note that the concept of additional spatial dimensions beyond the three we perceive is also explored in some theoretical frameworks, such as string theory and certain models in particle physics. However, these extra dimensions are often considered to be compactified or "curled up" at scales much smaller than we can directly observe, making their effects difficult to detect in our everyday experiences.