A Micro-Macro $1-\tau$ Closure: From Muon Spin to Galaxy Clusters at $R_{500}$Authors/CreatorsVallejos, José Fabián

DescriptionWe present a falsifiable micro-macro closure based on a finite-capacity vacuum characterized by a single universal response time $\tau$. The same micro-fixed $\tau$ that closes leptonic observables (including the muon sector) is shown here to govern gravitational equilibria at the cluster scale within the standard overdensity radius $R_{500}$.Using weak lensing and baryonic data for 40 LoCuSS galaxy clusters, we define a dimensionless spherical topology diagnostic $\xi$ that directly relates the lensing acceleration requirement to the baryonic Newtonian acceleration without invoking dark matter halos or readjusting $\tau$. The raw diagnostic exhibits a slight mass-dependent drift, which we demonstrate arises from weak lensing profile systematics and projection effects. A single global mass-centered mapping correction eliminates this drift, yielding a corrected topological factor $\xi_{top}$ consistent with a class-level horizontal band.All results are reported on a per-cluster basis, providing full audit tables and reproducible code. The analysis utilizes no per-object tuning, introduces no additional dynamical degrees of freedom, and preserves a closed $\tau \rightarrow a_* \rightarrow \Lambda_{eff}$ causal chain across scales. This work provides a direct empirical test of whether a single micro-fixed vacuum timescale can bridge leptonic physics with cluster-scale gravity.