Identifiability of metabolic resilience from sparse longitudinal metabolomics

Sparse and irregular longitudinal metabolomic measurements can make dynamical quantities numerically estimable without making them scientifically identifiable. We formulate effective-landscape inference as an observation-timescale inverse problem and evaluate its operating characteristics using stochastic systems with known ground truth and longitudinal stool metabolomics from the Integrative Human Microbiome Project. Across simulation ensembles, recovery of a known double-well topology declined sharply as observations became sparse, whereas the tested monostable controls did not generate spurious secondary minima. Findings establish an identifiability hierarchy: global topology requires sufficient within-subject state-space coverage, whereas local return descriptors remain vulnerable to bias from the observation process. The framework therefore shifts the emphasis from assigning stability labels to determining what a sampling design can support. It provides a basis for designing denser longitudinal experiments and for validating clinical and machine-learning studies in which sparse observations might otherwise be overinterpreted as evidence about underlying dynamics.