A One- 𝜏 τ Micro–Macro Closure from Muon Spin to Galaxy Clusters at 𝑅 500 R 500

We present a falsifiable micro–macro closure based on a finite-capacity vacuum characterized by a single universalresponse time τ. The same micro-fixed τ that closes leptonic observables (including the muon sector) is shown hereto govern cluster-scale gravitational equilibria at the standard overdensity radius R500. Using weak-lensing and baryonic data for 40 LoCuSS galaxy clusters, we define a dimensionless spherical topologydiagnostic ξ that directly relates the lensing acceleration requirement to the baryonic Newtonian accelerationwithout invoking dark matter halos or refitting τ. The raw diagnostic exhibits a mild mass-dependent drift, which we demonstrate to arise from weak-lensing profile and projection systematics. A single global, mass-centeredmapping correction removes this drift, yielding a corrected topology factor ξₜop consistent with a class-levelhorizontal band. All results are reported per cluster, with full audit tables and reproducible code provided. The analysis makes nouse of per-object tuning, introduces no additional dynamical degrees of freedom, and preserves a closed causal chainτ → a★ → Λₑff across scales. The work provides a direct empirical test of whether a single micro-fixed vacuumtimescale can bridge leptonic physics and cluster-scale gravity.