Age–sex heterogeneity among Russia’s indigenous small-numbered peoples: a census-based typology and the statistical core-region condition

Demographic structure does not determine intergenerational cultural continuity, but it conditions its opportunities and constraints. Using Rosstat’s 2020 All-Russian Population Census tabulations, this study assembles non-overlapping national and regional age–sex profiles for legally recognized Indigenous Small-Numbered Peoples of the Russian Federation. Three questions are addressed: which latent dimensions organize territorial variation in these profiles, whether a low-dimensional typology provides a defensible summary, and under what degree of territorial concentration a national profile can be used as a proxy for the largest regional concentration. The main specification transforms 15 age-group shares with a centered log-ratio procedure, adds overall and ages-20–39 sex ratios, and analyzes 103 ethnonym × territory profiles (N≥200) with principal component analysis and clustering. A separate core-region analysis compares national and core age–sex distributions with L1 distances. PC1 is a youth-to-ageing gradient, whereas PC2 captures male-skewed working-age structure. The first two principal components explain 65.0% of total variance. Silhouette diagnostics favor k=2 (0.457), but robustness checks show that this partition is only a pragmatic summary of a dominant continuum rather than evidence of two natural kinds. The main robust result is the continuum itself and the contrast between its younger and older poles, while intermediate cases remain soft assignments. The younger cluster (n=86) has a mean median age of 31.4 years and a mean ageing index of 26.2; the older cluster (n=17) has corresponding values of 48.1 and 231.0. National-vs.-core discrepancy declines systematically with core share. In this dataset and census framework, ethnonyms with core share around or above 0.85 have L1 distance no greater than 0.041; this value should be treated as an empirical rule of thumb rather than a universal threshold. The study contributes a reproducible statistical typology and an operational criterion for when national demographic profiles are, and are not, adequate proxies for territorially concentrated populations.