Hi Antony,
Sorry it took a while to reply. I have to translate the words into mathematics to understand them.
1. I'm not really sure what you mean by 3-dimensional information. Information is generally perceived to be numeric, i.e., independent of dimensionality. For example, if I communicate the statement 2 2 = 4, mathematical convention makes it unnecessary to answer which dimension the numbers live in. If I specify a dimensional context, e.g., I say "The natural numbers live on a 1-dimensional line," then I am mapping the geometry of the line to the continuum of dimensionless natural numbers. When we move up a dimension, to the 2-dimension plane of complex analysis with both real and imaginary lines, we get as a result both 3 and 4 dimensional analysis for free, because the complex plane is what mathematicians call algebraically closed. In other words, it allows 1 to 1 numerical mapping of every dimensionless point to every other point of the plane, sphere and four- dimensional hypersphere. So thinking it through, I guess you mean a bounded 3-dimensional ball of self interacting points? The BH event horizon, though, is still only 2-dimensional -- the surface of a ball -- so there is still the question of how, mechanically, to map your 3-dimensional information to the 2-dimensional surface, which is how the holographic principle (t'Hooft, Susskind) was born.
2. Maybe the foregoing is what you mean by "The astronaut can not receive information from inside the black hole. This is a point when information can only be BOTH received and revealed across 2-dimensions."?
3. "There ought to be a point, from a thought experiment point of view, where information can only be released, and deeper where it can only be received 1-dimensionally. Then at the singularity there are 0-dimensions." I can't get my mind around this -- relativity and Noether's theorem demand symmetry. That is why Hawking radiation was such a huge breakthrough in foundational terms -- the interaction of the BH with the outside world is no longer one-way, but allows information to escape via quantum uncertainty. The total evaporation of the BH should restore the total information "lost" behind the event horizon. So if any 0-D singularity ever existed, it would be annihilated (extinguished) in finite time. It couldn't be physical, therefore, and we would never know whether it existed or not.
4. "As mentioned the sequence allows 0 to be skipped over via -1, 1, 0, 1, 1 part via equivalence amongst other reasons." This would be more understandable in terms of complex analysis, where the unique point (0,0) allows a potential rotation in the plane with the result 0 0i. When one tries this with real analysis on the line R, "skipping over" a number looks too much like the famous cartoon where a theorist gets stuck and then declares, "Here a miracle occurs."
5. "The negative valued vertex is a quantum effect of the Black Hole that conserves space time between the black hole and the outside Universe." You explain that this makes the BH more stable. Before Hawking's result, most thought that this was the case -- everything goes in, nothing comes out. Even Hawking himself thought for years that thermal radiation (Hawking radiation) wouldn't allow the complete restoration of information going into the Black Hole. When one speaks of conservation of fundamental physical quantities -- mass/energy, angular momentum, time, what particle physicists call CPT conservation -- the symmetry has to be measured "backward and forward" to be physical. Time is the last mystery. The black hole you've described does not conserve time -- Hawking radiation does.
I am pleased to meet you, too -- all best in your research, and the contest!
Tom
