A geometric rs-fMRI connectome descriptor reveals individual stability without robust autism group differences

Autism spectrum disorder (ASD) has resisted reproducible case-control characterization in resting-state functional connectivity, leaving open whether reported group differences reflect genuine biology or methodological variability. We introduce a geometric framework that represents functional connectomes on the symmetric positive-definite Riemannian manifold and quantifies individual deviation as tangent-space dispersion, complemented by normative modeling of graph topology. Using the multi-site Autism Brain Imaging Data Exchange (ABIDE I) cohort (N=1035 subjects), we evaluate this descriptor under stringent robustness conditions and report three findings. First, individual connectome geometry is a stable, individually unique descriptor. The magnitude of a subject's deviation is highly reliable across split halves (intraclass correlation ICC[Formula: see text]) but is dominated by an acquisition-site scale, whereas its high-dimensional shape identifies subjects within-session with 98.9% accuracy once that scale is removed. Second, the case-control difference in dispersion is null and, by two one-sided equivalence tests against Cohen's d = 0.2, statistically equivalent to zero in all ABIDE I analysis cohorts (full cohort d = -0.007, N = 1035; strict cohort d = +0.038, N = 635); a nominal single-atlas effect (dispersion ratio 1.05, p = 0.046) does not survive multi-atlas reanalysis. Third, acquisition site explains 69% of dispersion variance while diagnosis explains 0.0001%; deviations form no discrete subtypes and do not predict symptom severity (minimum p=0.15 across tested graph-deviation predictors). Geometric dispersion is therefore a reproducible, individually unique connectome descriptor but not a case-control biomarker of ASD, which helps to explain the inconsistency of connectomic findings in autism.