The Floor That Never Reaches Zero: IE-001 and the Structural Minimum of Coupling Geometry

Establishes IE-001: the first invariant equation proving that alpha(d,beta) = 1 + d/(d+beta) bounds coupling to 1 < alpha < 2 for all positive d and beta. The floor at alpha=1 is structural not emergent; the asymptote at alpha=2 is unattainable. No system is ever fully decoupled from its geometric context. Mathematical foundations with five-domain physical interpretation. GCT Letters series.