Supplementary computational material: Residual-Λ band calculation (GCV)

Supplementary computational material: Residual-Λ band calculation (GCV) This release provides the numerical implementation and data products used to compute the residual cosmological constant (Λ) posterior (“Λ-band”) reported in the GCV Residual-Λ analysis. In the GR-exact branch of the Gauged Constant Vacuum-Mode (GCV) framework, local vacuum energy contributions do not gravitate and the effective cosmological constant Λ_{\rm eff} appears as a flux-fixed integration constant rather than a radiatively unstable low-energy parameter. The goal of this package is reproducibility and transparency: given an explicit near-zero discretuum model and conservative late-time viability criteria, the code constructs a posterior distribution for x≡Λ/Λobs,x \equiv \Lambda / \Lambda_{\rm obs},x≡Λ/Λobs, and extracts summary statistics including the median, 68% and 95% credible intervals, and the positive-Λ fraction f+f_{+}f+. Baseline model (as implemented): near-zero discretuum density ρ(x)∝∣x∣p\rho(x) \propto |x|^{p}ρ(x)∝∣x∣p (baseline p=0p = 0p=0) negative-Λ viability cut parameterized by κ\kappaκ via a toy recollapse mapping (baseline κ=7\kappa = 7κ=7) structure-suppression weight for x>0x > 0x>0:Wstruct(x)=exp⁡[−(x/xs)α]W_{\rm struct}(x) = \exp[-(x/x_{s})^{\alpha}]Wstruct(x)=exp[−(x/xs)α] (baseline α=1\alpha = 1α=1, xs=2.5x_{s} = 2.5xs=2.5) discretuum resolution cutoff xmin⁡=10−3x_{\min} = 10^{-3}xmin=10−3 Robustness grids are included exploring variations of the prior slope ppp, the recollapse threshold κ\kappaκ, and the structure-suppression scale xsx_{s}xs (and an optional lifetime-weight exponent γ\gammaγ used only as a stress test). This release does not claim a unique first-principles prediction of the observed cosmological constant. It provides a conditional typicality calculation under clearly stated assumptions within a radiatively stable, GR-exact framework. Contents: reference Python implementation (lambda_posterior_scan.py), baseline outputs (JSON), robustness grids (CSV), and paper-ready figure/table (PDF/TeX). Project homepage:https://johansson.digital Project overview and related material:https://github.com/gcv-framework/gcv-vacuum-energy Note: GitHub is used as a high-level discovery and overview hub only. For citation and archiving, please cite the relevant Zenodo concept DOI(s) for the scientific content.