Regulatory capacity is not a scalar: metrics, perturbations, and viability in network physiology

This is the authors' abstract. We don't add key points for this paper.

Biological regulatory capacity is commonly represented by a scalar: a summed biomarker index, standardized composite, risk count, or single recovery parameter. Such measures can be useful, but they do not identify capacity independently of the conditions under which they are constructed. This article argues that regulatory capacity is not an intrinsic scalar property of an organism. It is a conditional relation among the architecture and current state of a regulatory system, the perturbations that reach it, the metric or cost functional used to evaluate its response, the viability criterion, and the time horizon. Near an operating state, systems with identical eigenvalue spectra can incur different integrated burdens and reverse their apparent ranking when the perturbation channel or burden metric changes. For a declared quadratic burden in a stable local linearization, the observability Gramian associated with a virtual cost output represents accumulated weighted recovery burden, and the measurement map, burden-evaluation map, and latent state representation must be distinguished. For network physiology, allostasis, and allostatic-load measurement, routine choices about biomarkers, scaling, thresholds, and challenge paradigms are therefore constitutive assumptions rather than neutral preprocessing. Biological adaptation is likewise not equated with stability, compensation, recovery, or continued viability: it is indexed to a specified level of organization, protected function, reference or counterfactual, time horizon, and outcome or cost criterion. Regulatory Bandwidth is developed as a conditional perturbation-response profile rather than a universal scalar. Its contribution is a measurement architecture that requires the regulatory system, perturbation ecology, burden criterion, viability endpoint, and horizon to be declared before scalarization. The primary falsifiable comparison is between a flexible scalar-capacity model, which predicts one preserved ordering across declared perturbation classes, and a conditional-profile model tested on held-out sessions, contexts, or perturbations. Rejection of the scalar model supports conditional structure without establishing architectural heterogeneity, which requires a further shared-architecture comparison; this distinction bears directly on neurodiversity and person-environment fit. A worked orthostatic-challenge specification shows how measured outputs, constructed burden, viability, measurement error, and mechanistic interpretation can be separated in practice. The framework preserves the usefulness of scalar summaries while restricting the claims they can support.