From Performance to Representational Adequacy: A Representational Bootstrap Framework for Adaptive Biological Systems

Observable performance is commonly used to characterize biological systems, yet aggregated outputs may remain insufficient for uniquely resolving observational conditions, and richer multivariate representations may retain substantial ambiguity. This article proposes a representational bootstrap framework for adaptive biological systems. Bootstrap is used in a methodological and epistemological sense, not as statistical resampling. New analytical levels emerge when the active representation becomes insufficient for the question under investigation. The framework comprises five successive levels: observable performance, conceptual dynamic organization, exploratory multivariate representation, observed longitudinal centroid displacement, and internal approximation of observed displacement. Three previously reported gait-occlusion studies are used as a methodological case sequence rather than as new experimental evidence. The revised first study showed persistent static representational non-identifiability: neither the scalar score nor the exploratory embedding uniquely resolved the occlusal probes. The second study shifted the question toward M1-M2 centroid displacement in a common PCA representation. The third examined whether that observed representation-dependent transformation could be internally approximated by a simplified supervised model. The contribution is not a new algorithm, clinical protocol, or dataset. It is the formalization of a bootstrap methodology in which persistent explanatory insufficiency motivates reformulation of the scientific question and the emergence of progressively more adequate representations.