Yes, the three parts of the 'three' represent waking, dreaming and dreamless sleep. The dot beyond the veil represents turiya, the fourth state, the unceasing awareness to which the other three states appear. It is not Hyperspace but that (on)to which Hyperspace and other spaces appear.
A somewhat interesting aspect of AUM is that, if one were to chant the individual sounds in it (best done lying on one's back), 'A' resonates in the area of the abdomen (area of reproductive organs in the body, association with Brahma, the creative aspect), 'U' resonates in the chest area (lungs and heart, maintenance of life, Vishnu), and 'M' resonates in the forehead (brain, seat of the analytical and transformational/destructive aspect, Shiva).
Of course, one could easily get lost in fascination for such symbolism, philosophies, modifications, etc. The preference over here is to retain the attention on that to which all these diverse phenomena appear.
Here it is - right now. Start thinking about it and you miss it. ~ Huang-po