Perimeter-Law Memory in a Non-Hermitian Lattice with a Single Gain Site

We show that a non-Hermitian lattice with a single gain site amid uniform loss supports an exponentially long-lived geometric attractor. The memory lifetime obeys a perimeter law, log(tau_mem) ~ 2(L-1) log(1/epsilon), where epsilon = Omega/(eta+gamma) and L is the linear system size, governed by leakage through the nearest boundary. Two such attractors form a naturally degenerate qubit whose degeneracy is exact (gap ~ 10^{-15}) and robust to inter-chain coupling up to J = 4(eta+gamma). Two control parameters restore full rank of the projected information metric within the degenerate subspace, establishing complete controllability without breaking lifetime protection. The Wilczek-Zee connection is non-Abelian but flat; control is dynamical, not topological. For epsilon = 0.01 and L = 10, the extrapolated qubit lifetime exceeds 10^{36} within the effective non-Hermitian description.