I.R30 — Duality and Atoms

Vertical-Horizontal Duality and Set-Theoretic Atoms: gamma explores depth (one prime, all powers), eta explores breadth (all primes, one power), mirroring the fiber-base decomposition. Set(eta_1) = canonical prime set. For any prime p, Set(alpha_p) = {alpha_1, alpha_p} — primes are set-theoretic atoms whose only divisors are 1 and themselves.