A Data-Driven Environmental Model Closes the HerS-3 Mass Budget Without a Localized SE Halo

We present a comprehensive analysis of the HerS-3 gravitational lens system using data-
driven environmental modeling. With zl≈1.0, zs=3.0607, θE=3.7′′, ME=5.728 × 1012M⊙,
Mb=4.563 × 1012M⊙, and κext=0.1876 ± 0.0246, we obtain κmin = 0.0158 (Excellent; 0.040
at 1σ). Our decision thresholds (Excellent if κmin ≤ 0.30; Good if 0.30 < κmin ≤ 0.40)
are anchored in mock simulations spanning 100 analogs. Head-to-head model comparison
favors our approach: ∆AIC= −3.8, ∆BIC= −2.1 relative to the SE-halo model. Extensive
stability tests (κext depth/R-cut variations, Mb systematics including IMF/M/L/dust/PSF,
local-environment member reattribution, and joint {κext, Mb, ME} prior sweeps) confirm
robustness.
Shear priors are anchored in weak-lensing studies of similar environments.
Statistical caveats are explicit: shear-LOS alignment shows only weak evidence (Rayleigh
p=0.21). Full reproducibility package with masks, PSF, and unified scripts provided