An environment-dependent weak-lensing residual in KiDS: a covariance-audited measurement with strict null tests

We present a covariance-audited measurement of an environment-dependent weak-lensing differential signal in the Kilo-Degree Survey (KiDS). Using a bright photometric lens sample (≈9. 9×10⁵ lenses in 27 tomographic slices), we split lenses into low- and high-environment quintiles based on a projected density proxy and measure excess surface density profiles ΔΣ (R). We form the differential signal ΔΔΣ (R) =ΔΣₗow (R) −ΔΣₕigh (R) across 15 angular bins (R≈0. 65–18 arcmin) and use the 45°-rotated cross component as the primary null channel. Full per-slice jackknife covariance matrices are propagated throughout and explicitly audited for completeness, conditioning, and inversion stability (27/27 slices pass; condition numbers up to ~4×10³; results invariant under diagonal-jitter scans). We find that the stacked tangential channel deviates from an R-matched random-points null baseline under the same constant-offset statistic (Δâ=−1. 001×10^−3 in the internal Σcrit-weighted estimator normalization; Δχ²ᵣed=+1. 108 relative to the null), while the cross channel remains near null (Δχ²ᵣed=+0. 051). A dedicated systematics suite (PSF-leakage template marginalization, random-points null, boost-factor audit, bin-centre mismatch) does not identify a tested additive systematic capable of explaining the tangential residual; the PSF template explains ≲7% of the signal RMS and does not reduce χ²ᵣed. Matched and SFR-controlled catalogue variants are provided for confounder control and independent re-analysis; a phenomenological template comparison to external-field lensing templates is included as a shape-basis summary. New in this version: This release is a cleaned, submission-ready manuscript update with consolidated notation, clarified estimator/units handling (internal normalization vs. shear units), tightened baseline definitions, and updated metadata (author, affiliations, and repository link), plus minor text edits to improve traceability and reproducibility.