Python Code for Figures 1–9 of "GR + Modified Euler Tests of Dark-Matter Motions with RSD, Lensing, and Gravitational Redshift" (Version 3)

This repository provides the Python source code used to generate Figures 1–9 of the manuscript: GR + Modified Euler Tests of Dark-Matter Motions with RSD, Lensing, and Gravitational Redshift The code supports a reproducible visualization and analysis pipeline for a phenomenological GR + modified Euler framework for dark-matter motion. The manuscript tests whether the dark-matter Euler equation may receive effective force-like and friction-like corrections while the metric sector remains consistent with General Relativity, Φ=Ψ\Phi=\PsiΦ=Ψ. The scripts generate posterior-style visualizations, response-function trend plots, correlation matrices, null-test residuals, and model-comparison figures associated with the joint use of: Redshift-space distortions (RSD) Weak gravitational lensing / Weyl-potential probes Relativistic gravitational-redshift / Ψdir\Psi_{\rm dir}Ψdir estimators The code is intended for transparency, reproducibility, and figure-level validation of the manuscript’s phenomenological parameterization. What is New in Version 3 Version 3 updates the figure-generation package to match the revised manuscript and referee-response version. The main changes are: Corrected Figure 2 and Figure 9 response-trend scriptsThe Γinfo(z,k)\Gamma_{\rm info}(z,k)Γinfo(z,k) implementation in the trend-plot scripts has been corrected to follow the finite-range Euler-sector ansatz used in the manuscript: Γinfo(z,k)=gI2χ0(1+z)−pk2(1+z)2mI2+k2(1+z)2.\Gamma_{\rm info}(z,k) = g_I^2\chi_0(1+z)^{-p} \frac{k^2(1+z)^2}{m_I^2+k^2(1+z)^2}.Γinfo(z,k)=gI2χ0(1+z)−pmI2+k2(1+z)2k2(1+z)2. The corrected curves now show the intended low-kkk suppression and high-kkk saturation. Updated θinfo(z)\theta_{\rm info}(z)θinfo(z) trend consistencyThe Figure 2 fallback/synthetic posterior has been updated so that θinfo(z)=θ0(1+z)q\theta_{\rm info}(z)=\theta_0(1+z)^qθinfo(z)=θ0(1+z)q is consistent with the manuscript’s Table III parameter values, especially the positive posterior value of qqq. This removes the previous inconsistency in which the Figure 2 θinfo(z)\theta_{\rm info}(z)θinfo(z) panel appeared nearly flat while Figure 9 and Table III implied an increasing redshift trend. Harmonized Figure 2 and Figure 9 visual behaviorThe response-function trend figures now consistently display: Γinfo(z,k)\Gamma_{\rm info}(z,k)Γinfo(z,k): low-kkk suppression, transition near k⋆(z)=mI/(1+z)k_\star(z)=m_I/(1+z)k⋆(z)=mI/(1+z), and high-kkk saturation θinfo(z)\theta_{\rm info}(z)θinfo(z): redshift-dependent growth-drag behavior consistent with the posterior parameterization Updated captions and labeling consistencyFigure labeling and trend descriptions have been revised to avoid overstating the finite-range scale break as a model-independent prediction. The scale break is now treated as a characteristic diagnostic of the finite-range Euler-sector ansatz. Improved reproducibility safeguardsThe updated scripts include physical clipping for parameters such as gIg_IgI, mIm_ImI, χ0\chi_0χ0, and θ0\theta_0θ0, reducing failures in log-scale plotting and avoiding unphysical fallback samples. Included Scripts This release contains Python scripts for generating the figure set associated with the manuscript, including: fig_corner_IG_full_hpd.py fig_corner_IG_hp_kde.py fig_corner_MG_full_hpd.py fig_corr_params_heatmap.py fig_corr_data_block.py fig_resid_slip_zk.py fig_resid_dfgrowth.py fig_trends_gamma_theta.py fig_trend_panels_gamma_theta.py Together these scripts generate the main and appendix figures, including posterior corner plots, correlation matrices, slip-null residuals, EP-like differential-growth residuals, and posterior-predicted trends of the IG response functions. Technical Details Language: Python 3.9 or later recommended Core libraries: NumPy SciPy Matplotlib Pillow, for optional image/PDF stitching corner, optional for posterior corner plots emcee or dynesty, optional if posterior sampling is regenerated rather than read from stored samples The numerical and plotting components include: Modified Euler response-function visualization Posterior-predictive trend propagation Correlation-matrix plotting Null-test residual visualization Posterior corner and HPD/KDE contour plotting Publication-quality figure export in PNG/PDF formats Reproducibility Note The scripts are designed to generate the manuscript figures from posterior sample files when available. If posterior sample files are not present, selected scripts use documented synthetic fallback samples for visualization and testing. In Version 3, these fallback samples have been updated to be consistent with the revised manuscript’s reported parameter values, particularly for the Figure 2 and Figure 9 response trends. The code is provided for figure-level reproducibility and transparency of the plotting and phenomenological-analysis workflow. It should be used together with the corresponding manuscript version and its stated assumptions, priors, and compressed-likelihood setup. Related Manuscript GR + Modified Euler Tests of Dark-Matter Motions with RSD, Lensing, and Gravitational Redshift A preprint version of the manuscript is publicly available on Zenodo. If applicable, please cite both the manuscript DOI and this code repository DOI when using or adapting the scripts.