A Theory-Neutral Gravitational Lensing Test of Environmental History Dependence at Fixed Baryonic Mass — Cluster-Scale Pilot Protocol for Distinguishing Assembly Bias from History-Dependent Effective Gravity

We propose a theory-neutral observational protocol to test whether the weak-lensing mass of galaxy clusters depends on environmental history at fixed baryonic mass. The central question is empirical and falsifiable: among clusters with comparable baryonic content, do systems with richer dynamical and thermodynamic histories exhibit systematically different weak-lensing mass estimates? Within ΛCDM, any detected trend constrains halo assembly bias and baryon–halo stochasticity. Within alternative frameworks, it tests whether effective gravitational mass contains a cumulative environmental component beyond present baryonic content. A null result places an upper limit on any such history dependence. The protocol requires strict data-lineage independence between the lensing output channel and environmental-history input channel, decomposes history into three distinct axes (merger/disturbance, thermodynamic relaxation, large-scale environment) tested independently before composite construction, treats redshift as a control variable rather than a proxy component, and introduces a residual-excess test against matched ΛCDM simulations as the primary discrimination layer. A secondary hydrostatic-to-lensing mass comparison provides additional leverage against purely baryonic explanations. Preregistration requirements, robustness checks, and explicit falsification criteria are defined. This work refines and extends the exploratory cluster-scale correlation reported in V80 (CLASH Environmental Axis Test) into a methodologically stricter, theory-neutral, and independently reproducible framework.