IV.P155 — Multiplicative Closure

Every entry in the coupling ledger is a product of powers of iota_tau and (1 +/- iota_tau). No irrational factor, transcendental prefactor, or fitting parameter enters. All ten entries lie in Q[iota_tau, (1-iota_tau)^{-1}, (1+iota_tau)^{-1}], verified by inspection of the explicit formulas.