The Biological q10 Tail as a Layered System: Rich-Club Scaffold, SST Actuation, and Thalamocortical Thickening

Abstract Recent extensions of the Curvature Adaptation Hypothesis (CAH) have shifted attention from whole-network mean geometry to the lower-curvature tail as a potentially load-bearing scaffold for constrained transport. In this context, the q10 regime has emerged as a candidate substructure carrying disproportionate integrative burden in abstract and simulated networks. This raises a biological question: what, if anything, plays an analogous role in the brain? This perspective proposes that the biological realization of q10 is unlikely to be unitary. Instead, it may be layered across multiple interacting systems. Rich-club architecture and long-range fasciculi are argued to provide a candidate structural scaffold for high-value integrative routes. Somatostatin-expressing (SST) interneurons are proposed as a candidate geometric actuator, regulating local access to such routes through dendritic control. Diffuse corticothalamic or matrix-thalamic systems are proposed as a candidate temporal thickener, helping stabilize and distribute that access across wider cortical territory and behaviorally relevant timescales. This layered view generates structured predictions and dissociations, reframes the search for q10 in the brain as a cross-scale research program rather than a hunt for a single hidden subnetwork, and clarifies how anatomy, inhibitory control, and thalamocortical coordination might jointly support transport-efficient integration. Summary This perspective paper develops a biologically grounded hypothesis for how the q10 lower-curvature tail may be realized in the brain. Building on the Curvature Adaptation Hypothesis (CAH) and Beyond Mean Curvature, it argues that q10 is unlikely to correspond to a single hidden subnetwork. Instead, its biological realization may be layered across multiple interacting systems. The paper proposes that rich-club architecture and long-range fasciculi provide a candidate structural scaffold, SST interneurons provide a candidate geometric actuator through dendritic gating, and diffuse corticothalamic or matrix-thalamic systems provide a candidate temporal thickener that helps sustain and coordinate access to transport-efficient integrative routes. Rather than claiming discovery, the paper offers a cross-scale research program that reframes the search for q10 in the brain around three functional components: scaffold, actuation, and thickening. The goal is to make the biological problem of q10 more precise, more testable, and more anatomically grounded than broader alternatives. Related Works Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. Zenodo. https://doi.org/10.5281/zenodo.18615180 Pender, M. A. (2026). Beyond Mean Curvature: Lower-Tail Routing Structure in Controlled Hierarchical Networks. https://doi.org/10.5281/zenodo.19324674