An environment-dependent weak-lensing residual in KiDS: a covariance-audited measurement with source-redshift, intrinsic-alignment, and selection stress tests

We present a covariance-audited measurement of an environment-dependent weak-lensing differential signal in the Kilo-Degree Survey (KiDS), extended by a coordinated set of targeted stress tests aimed at the most plausible non- detection explanations. A bright photometric lens sample (≈9.9 ×105 lenses, 27 tomographic slices) is split into low- ¯ and high-environment quintiles (q0 vs. q4) via a projected density-proxy field (ηk ≡Σk / Σk−1). We compute excess surface density profiles ∆Σ(R) and form the differential signal ∆∆Σ(R) = ∆Σq0 (R)−∆Σq4 (R) across 15 angular bins (R≈0.65–18 arcmin), using the cross component as the primary null channel. Full per-slice jackknife covariance matrices are propagated throughout; their completeness, condition numbers, and inversion stability are verified by an explicit audit (27/27 slices pass; condition numbers up to∼4 ×103; a diagonal-jitter scan confirms numerical invariance). The stacked tangential channel deviates from an R-matched random-points null baseline under the constant-offset statistic (∆ˆ a =−1.001 ×10−3 in the internal Σcrit-weighted estimator normalisation; ∆χ2 red = +1.108), while the cross channel shows near-null deviation (∆χ2 red = +0.051). Thematchedlow-andhigh-environmentlenssamplesareextremelywellbalancedinphotometricredshift,|∆z|/(1+ ¯ z) = 3.06 ×10−4. A dedicated source-redshift stress rerun shows that the tangential pattern is retained under stricter background cuts ZB >zl +0.2 and ZB >zl +0.3, with RMS amplitudes 1.13 and 1.29 times the baseline ZB >zl +0.1 value, while a foreground-source null reaches only 0.42 of the baseline tangential RMS. A differential PSF template remains subdominant at the 3–6 % RMS level for the background selections. Combining the radial source-density ratio with the boost-factor asymmetry, a deliberately conservative multiplicative stress rescaling moves the tangential RMS at the tens-of-percent level but does not remove the pattern or convert it into the cross-channel/foreground morphology. A red/blue source-colour split gives tangential RMS ratios red/blue = 1.29 and 1.06 for the +0.1 and +0.3 cuts, and an empirical foreground-red IA-template absorbs only 5–10 % of the background-selected RMS. We do not claim a unique modified-gravity interpretation. Intrinsic alignments, baryonic feedback, halo occupation, satellite fraction, and assembly bias remain explicit physical comparison classes. Matched and SFR-controlled cata- loguevariantsarereleasedwiththereproducibilitypackagetoenableindependentre-analysisandextendedhalo-proxy controls. A phenomenological shape-basis template comparison is provided in Appendix E.