Pathway Identifiability under Partial Metabolomics via JL-Stabilized FGW Alignment and Measurement-Driven Disambiguation

This work introduces a general computational framework for identifiability analysis and measurement prioritization in partially observed biological networks. The framework is motivated by metabolomics, where incomplete metabolite coverage induces structural ambiguity in pathway interpretation, but is formulated independently of any specific data modality. Biological systems are represented as condition-aware graphs containing both observed and latent nodes. Rather than imputing missing measurements or enumerating latent completions, missingness is encoded explicitly as uncertainty in node features. Pathway states across conditions are compared using a geometry-aware alignment operator based on Fused Gromov–Wasserstein optimal transport, stabilized via Johnson–Lindenstrauss projection to ensure reproducible distance geometry under high-dimensional sparsity. Pathway underdetermination is quantified using a composite functional that combines transport entropy, alignment instability, and a structural risk index capturing both branching-driven ambiguity and bottleneck fragility. Building on this diagnostic, the framework introduces a computable measurement-impact estimator that prioritizes the next measurement expected to maximally reduce ambiguity, without enumerating latent states. Measurement recommendations are validated using a falsifiable synthetic masking protocol with regret-based evaluation. While metabolomics provides a particularly hostile test case due to extreme partial observability, the framework is modality-agnostic and applies to other domains such as single-cell and spatial biology, where structured missingness and ambiguous state correspondence are fundamental challenges. This submission represents a methodological framework intended to support epistemically honest interpretation and experimental design under partial observability, rather than to provide definitive mechanistic or causal inference.