Extreme-Tail Radial Differentiation in HST Chromosome Maps of Galactic Globular Clusters: A Link to Central Structural State

Chromosome maps (ChMs) reveal multiple stellar populations in globular clusters (GCs), but radial trends can depend on how overlapping structures are partitioned. We analyse 56 Galactic GCs with Hubble Space Telescope UV Globular Cluster Survey (HUGS) photometry, separating the stability of star-by-star Gaussian-mixture assignments from that of radial statistics. Strict two-family assignments are stable in only 11/55 eligible clusters, whereas the posterior-weighted radial contrast is reproducible for 34/55. In this radial-stability sample, none of four pre-specified broad-family tests shows a robust association with compactness or half-mass relaxation time. By contrast, the label-free absolute median-radius separation between the lowest and highest 30 per cent of normalized ChM pseudocolour increases with compactness (N=34, ρ=0.500, permutation p=0.00256) and remains positive after F814W matching and common-footprint restrictions. Secondary tests show no comparable monotonic ordering with remaining-mass fraction, a present-day dynamical-age proxy, or the atlas-based global second-generation fraction. Larger amplitudes instead occur at greater compactness, higher central density, and shorter core-relaxation time. Because these central variables are strongly collinear, we interpret them as a common structural-state axis rather than unique causal drivers. Thus, the magnitude—not a universal direction—of extreme-tail radial differentiation is linked to present-day central structural state.