Triangle redundancy as a cross-circuit architectural regularity: a Topostability analysis of thirteen neural circuits

We apply Topostability, a graph-theoretic framework based on triangle density per edge (tri(e)), to thirteen mammalian neural circuits spanning motor, limbic, sensory, autonomic, and cognitive systems. Each edge is classified into one of three structural regimes (always fragile, fragile, or stable), and a scalar Fragility Index (FI) is derived for each circuit. Using a pre-specified functional taxonomy, circuits are assigned to three classes: rapid selection/precision (Class A), intermediate regulation/encoding (Class B), and integration/homeostasis (Class C). Across nine circuits with robust connectivity models, FI followed the predicted ordering: Class A (median 47.2), Class B (38.9), Class C (34.8). A Kruskal-Wallis test on Tier 1 circuits yielded H = 7.06, p = 0.029; a permutation test (1,000 iterations) confirmed that the pre-specified assignment produces significantly greater class separation than chance (p = 0.002). These results are consistent with a candidate cross-circuit architectural regularity linking triangle redundancy to computational regime.