Bull's-eye, Doug! I expect that science press attention will start picking up steam on this news by the time the academic year rolls in. If Ray Chiao is on board with these results, the buzz will be all the stronger.
I've been drafting a paper to better explain the "middle value" relation that my essay addresses, and which ties into Blencowe's Gaussian ball. I'm seeing the ball as the potential of massless energy (graviton spin 2 particles) with Gaussian normal distribution:
Using induction and the continuum hypothesis, I find that because the fixed congruence condition of twin primes, P_1 = P_2 (mod 2) generalizes to all odd primes*, the smallest magnitude -- i.e., any twin prime pair -- contains the largest differential (infinity), which is the cardinality of the continuum. For example, the set {17,19} with median 18 partitioned {17,18} {18,19} has no zero point as would be the case with {18,18} because the median on R_ has no clone.
The "no cloning" theorem of quantum mechanics** which rejects the middle value is relevant here, whether we speak of prime integers or discrete particles -- because when we expand the magnitude to any arbitrary P_1, P_2, the mean is a definite finite point. For example, take the set {3, 119} whose mean is 58. In the previous example mean = median, so there is no definite point that partitions the integers, while the case of the relative state 3 = 119 (mod 2) gives us the definite state {3, 58, 119}. Long story short -- and leaving out the complex analysis needed to prove the case -- the implication is that the existence of 2 relative states implies 3 definite states.
All Best,
Tom
* Ray, T. proceedings ICCS 2006
** Wooters, Zurek