Erratum and Re-evaluation: Constraints on the ΨTMG Modified Gravity Model using Planck 2018 and LSS Data

This release serves as an official Erratum and update to the previously published cosmological constraints on the ΨTMG (Modified Gravity) model. The Correction: In the initial v1 release, an error in the implementation within the Boltzmann solver (CLASS) artificially allowed the model to shift the sound horizon (rₛ) at recombination, creating a false resolution to the Hubble (H₀) tension. The code has been fully corrected to properly decouple the background thermodynamics from the spatial modified gravity perturbations. New Results & Conclusions: After re-running full MCMC chains via Cobaya against Planck 2018 (TT, TE, EE + lensing), BAO, and Pantheon+ data, we conclude the following: Baseline Consistency: The corrected ΨTMG model is highly consistent with standard ΛCDM. The background expansion remains strictly constrained by the CMB, yielding H₀ = 68. 12 ± 0. 45 km/s/Mpc. Strict Parameter Constraints: The modified gravity parameter is heavily constrained to α = 0. 0001 ± 0. 0008 (at 1σ), showing no significant deviation from General Relativity in the early universe. The S₈ Tension Aspect: While H₀ remains unaffected, the corrected model demonstrates a slight widening and downward shift in the S₈ parameter space (S₈ = 0. 830 ± 0. 012) compared to the ΛCDM baseline, offering a potential pathway to ease structural tensions with Late-Time Weak Lensing surveys. Files Included: VERDICTFINALS8. png: The updated 4-parameter triangle plot (H₀, Ωₘ, S₈, α). deliverableₑrratumₚsitmg. zip: Contains the updated. yaml configuration files and the fully post-processed MCMC chains (. post. 1. txt) for both ΨTMG and the ΛCDM baseline for full reproducibility. erratumₙote. pdf: A detailed breakdown of the code correction and physical interpretation.