Interaction-Uniform Analytic Stationary Response in Dissipative Quantum Spin Lattices

We study stationary response in amplitude-damped spin lattices with pair driving,nearest-neighbor hopping, and arbitrary real diagonal fields and interactions. The centralresult is an interaction-dressed operator construction: diagonal energies enter an invariantclass of bounded occupation-dependent phases, yielding stationary expectations analyticin complex drive and hopping, uniformly in volume and interaction strength. On rings,one weighted-atom estimate gives |g| + |J| < 3375γ/48668; an independent one-dimensionalfinite-state charging certificate gives (48/5)|J| + (219488/6875)|g| < γ. Their union extendsthe sufficient analytic domain to J = 0.1γ at small nonzero drive. Separately, for eachprescribed drive order and arbitrary fixed hopping, a recycling-inclusive, connected-sourceargument bounds local response coefficients and connected density correlations independentlyof system size and all diagonal energies, and establishes coefficientwise thermodynamic limitson periodic lattices. At arbitrary real hopping and drive, a weighted number-balance identityyields occupation clamping and localization from a pumped bond, both in stationary statesand at every time when the initial state is the vacuum. On rings, local Poisson estimates alsogive a Gevrey-2 real-drive remainder for arbitrary fixed hopping. Exact rational coefficientsand full-Liouvillian finite-ring calculations illustrate the distinction between uniform boundsand interaction-dependent physical densities. These statements apply to different parameterregimes and do not assert strong-hopping complex-drive analyticity.ZIP File: Executable exact-rational verification source, a finite-state 1,024-state/3,520-transition certificate, stationary-response coefficient records, untruncated numerical 10-spin Liouvillian benchmark data from two independent solvers, figure-generation files, and the 45-page manuscript source. Includes verification limitations and reproducibility guide.