Chapter 34: The Master Constant ι_τ = 2/(π + e)

Throughout Part IV we classified primes into two sectors — B-dominant and C-dominant — according to their behavior in the prime bipolar partition . This classification is not merely qualitative: the ratio of B-dominant to C-dominant primes converges to a fixed number as we range over all primes. This chapter introduces that number, the master constant ι_τ = 2/(π + e) ≈ 0.341304, and explains its structural role as a parametrization of the asymmetry between the two lemniscate lobes. The full analytic proof of convergence belongs to Book II; here we state the result, motivate it, and verify it numerically.