Forward-modeling pipeline used to generate simulated samples of galaxy clusters from input parameters. We began with a set of input cosmological parameters: Ω_m, σ₈, and H₀. From these parameters, we generated cluster masses within a fiducial volume slice of fixed redshift (see Section 3.1) using the HMF (see Section 3.2). Before applying the scaling relations, we ensured that the cluster masses were defined consistently with the cosmology associated with these relations (see Section 3.3). Luminosities and temperatures were then derived from these masses through scaling relations (see Section 3.4). We applied a k-correction to derive observer-frame luminosities (see Section 3.5) and used a β-model to rescale the predicted flux into a fixed physical aperture (see Section 3.6). Finally, we applied the selection function of the observed sample to the relevant observables to produce a mock catalog of galaxy clusters that is directly comparable with the observed sample (see Section 3.7).