There is a major collection of axons connecting the two sides of the cerebral cortex, the corpus callosum. It is not clear why any one part of the brain would be particularly important for connecting the non-material Phantom Core to the physical structures of the brain, but the Lyricus Teaching does emphasize the link between consciousness and the soul. The corpus callosum allows us to coordinate brain functions that are differently distributed between the two sides of the brain....probably most things we can become aware of have a "reflection" in the data stream of the corpus callosum.
"Even in the quiet moments of your life when you are staring through a window or reading a book, there is a great universe of experience that is perceived by this phantom core, and every miniature detail is faithfully recorded and transmitted to the soul." (Lyricus Discourse 3)
This suggests to me that the Phantom Core may have access to all of the "great universe of experience". If everything being transmitted through the corpus callosum was passed on to the soul by the Phantom Core, that might well constitute a good record of everything available to our personal experience.