Chapter 29: Polarized Omega-Germs

the relevant chapter constructed omega-tails as the pre-topological boundary data of τ. This chapter introduces the decisive structural feature: polarization. At each finite refinement depth, the local fiber of an omega-germ has two channel quotients — B_n and C_n — forming a local fiber product T_n = B_n × C_n. A germ is polarized when one channel eventually freezes while the other continues to refine. B-polarized germs correspond to B-dominant primes; C-polarized germs to C-dominant primes. The unique germ where neither channel freezes is the crossing-point germ, identified with the beacon ω.