Peak statistics are weak lensing's census of the densest structures: count the peaks in a smoothed convergence map as a function of height, and an almost-Gaussian initial field evolved under gravity predicts the result through halo models and simulations (Bardeen et al. 1986; Coles 2002). Peaks at high signal-to-noise correspond mostly to individual massive halos along the line of sight, so their abundance is a direct probe of how steep and how concentrated the deepest potential wells really are.
Several analyses of galaxy and shear maps report a deficit: fewer high peaks, or a peak-height distribution shifted from the standard prediction, once the model is tuned to match the CMB and cluster counts (Peacock and Dodds 1996; Hoekstra 2001). The discrepancy is structurally awkward for ΛCDM because peak counts are tied to the NFW profile shape that collisionless N-body relaxation makes nearly inevitable: cuspy, concentrated halos produce sharp tall peaks, so a peak deficit hints either at smoother mass profiles than CDM particles allow, at strong baryonic feedback redistributing mass, or at line-of-sight projection physics outside the halo model.
The standing connects to the wider lensing sector. The peak deficit points the same direction as the S8 tension and the cluster lensing anomalies: the lensing sky is not distributed the way CDM-particle halos say it should be. Euclid, LSST, and Roman will measure peak functions at percent-level precision across thousands of square degrees, with enough statistics to test not just the abundance but the orientation distribution of the peaks themselves.