Shared NADPH regeneration sets sharp limits on joint glutathione and thioredoxin service

Two antioxidant branches that operate adequately in separate preparations need not meet the same branch-resolved requirements when they are coupled to a single NADPH regeneration system. We study a maintained-peroxide subsystem of published redox kinetics that retains finite enzyme and carrier inventories, including enzyme-bound glutathione. Exact elimination of the private states gives, for each branch, a positive quadratic carrier response and a strictly increasing service current as a function of the shared NADPH concentration. Against a strictly decreasing regeneration current this yields a necessary and sufficient condition for joint service, an explicit and attained minimum regeneration capacity, a reconstruction of every steady-state species, and uniqueness of the full joint steady state. We prove that a finite regeneration repair exists exactly when each quota lies strictly below its branch ceiling current, and we identify the exact deficit of a quota-only capacity estimate as kinetic overdelivery. For declared nominal parameters and design quotas of $10$ and $4$ $\mu\mathrm{M}\,\mathrm{s}^{-1}$, both isolated preparations succeed while their joint preparation fails at one tenth of the reference regeneration capacity; the attained minimum requires a certified $13.71266$–$13.71268\%$ increase over that setting. Allowing one enzyme inventory to change attains the quota-only bound exactly, with a $3.3727\%$ reduction in the glutathione peroxidase pool, and we prove a matching lower bound over every admitted redesign of that branch. The decision criterion, the separate-preparation comparison, the uniqueness and ceiling theorems and the constructive redesign are checked in Lean 4. We also delimit the result: we give the exact interval criterion that replaces the threshold when branch service is not monotone, an explicit analytic example in which excess regeneration destroys service without bistability, and a sign obstruction showing that the eight-variable kinetics admit no orthant order making them cooperative near the boundary equilibrium. The result concerns kinetic service in a declared maintained system. It is not a claim about whole-cell protection, clinical benefit, or thermodynamic incompatibility.