Gravitational Lensing as Discrete-Cell Optical Refraction: A Quantitative Comparison with Published Weak-Lensing Measurements of the Coma Cluster

This preprint investigates whether weak gravitational lensing in the Coma cluster (Abell 1656) can be described as an effective optical refraction phenomenon within the Planck Gravity (PG) theoretical system, without invoking non-baryonic dark matter. Serving as a direct continuation of our preceding X-ray hydrostatic study of the Coma cluster ("Resolving the Coma Cluster Mass Discrepancy Without Dark Matter: Multi-Layer Field Overlap and Apparent Ruler Scaling in the Planck Gravity Theoretical System", DOI: 10.5281/zenodo.24130723) and the foundational discrete-spacetime framework (DOI: 10.5281/zenodo.22995823), this work holds the four Coma radial scaling parameters strictly fixed (α = 2.561316, R_σ = 0.148961 Mpc, p = 0.618123, β = 0.501249) with zero re-fitting to lensing data. Key Methodology & Quantitative Findings:- Discrete-Cell Optical Index: Defines the effective PG cell-field potential Φ_PG(r) = −G ∫_r^∞ [M_baryon(<s) σ_local²(s) / s²] ds with boundary condition Φ_PG(∞) = 0, yielding a positive refractive index n_PG(r) = 1 − 2Φ_PG(r)/c² > 1 across all radii and resolving sign-inversion issues at the cluster outskirts.- Vector & High-Resolution Data Extraction: Digitizes two independent published tangential-shear profiles—high-resolution raster digitization of CFHT core observations by Gavazzi et al. (2009) and direct PDF vector coordinate extraction of wide-field SDSS DR5 observations by Kubo et al. (2007)—applying each survey's specific critical surface density (Σ_crit = 1.69 × 10^16 h_70 M_sun Mpc^-2 and 2.6299 × 10^16 M_sun Mpc^-2, respectively).- Fixed-Parameter Comparison Results: Using the projected effective-mass weak-lensing relation and diagonal 1σ plotted uncertainties, the comparison yields χ² ≈ 8.03 across all six Gavazzi et al. points (0.011–0.518 Mpc; decreasing to χ² ≈ 5.04 for the outer five points beyond 0.02 Mpc) and χ² ≈ 14.09 across all six Kubo et al. points (1.73–13.80 Mpc; χ²_A ≈ 6.61 for R ≤ 4 Mpc and χ²_B ≈ 7.47 for R > 4 Mpc). This manuscript establishes a transparent, reproducible, and falsifiable observational test protocol, explicitly outlining the methodological requirements—including full covariance matrices, source-redshift weighting, and independent nonlinear Eikonal ray-tracing verification—for future precision tests. Part of the Planck Gravity Theoretical System Series:- Foundational System: https://doi.org/10.5281/zenodo.22995823- Coma Cluster X-Ray Hydrostatic Study (Part 1): https://doi.org/10.5281/zenodo.24130723