A Finite-Capacity Bound of the Vacuum: From Muon Precision to Galaxy-Cluster Offsets.

We present a single operator-level framework in which the physical vacuum is endowed withfinite response capacity and finite memory. Once fixed in the microscopic sector byprecision observables, the operator admits no freedom at larger scales. Anchored by the muon anomalous magnetic moment, the vacuum relaxation time is shownto impose a strict bound on macroscopic lensing--baryon offsets in colliding galaxy clusters. For a given merger, the offset magnitude is not a fit parameter: it is uniquely determinedby the event demand and by vacuum constants already fixed at the quantum level. The same operator is then tested in an independent meso-scale regime. In the solar interior, finite vacuum response induces a sign-definite transport impedance under sustained radiativeflow, providing a non-phenomenological resolution of the solar abundance tension withoutmodifying stellar microphysics, opacity tables, or nuclear reaction rates. Taken together, these results establish a continuous micro--meso--macro chain governed bya single vacuum response operator. Agreement across scales is not enforced by calibrationbut required by consistency; failure at any scale falsifies the framework as a whole.