A No-Go Framework for Coarse-Grained Effect Prediction in Boron Neutron Capture Therapy: Structural Identifiability Limits and Microscopic Coverage

Abstract: We establish when coarse-grained observables uniquely determine an expectation-based biological response in boron neutron capture therapy (BNCT). Microscopic target populations are represented by probability distributions, while retained observables are finitely many population-averaged linear descriptors. For an admissible class containing all finitely supported microscopic distributions, exact distribution-free identification holds if and only if the single-target response kernel lies in the span of the constant function and retained descriptors. Thus mean dose, mixed-field component means, and finite moment sets are not generally sufficient under unrestricted microscopic heterogeneity. We also derive irreducible ambiguity and approximation bounds, sharp partial-identification intervals for bounded non-increasing convex survival kernels, a treatment-ranking criterion, and lower-tail and high-exposure bounds. A fixed-total-exposure temporal model distinguishes transient re-sampling from persistent target-specific underexposure, and a marked-Poisson model shows that separate frequency and event-quality marginals need not determine survival. The framework clarifies which microscopic information is lost through BNCT coarse-graining while leaving room for approximation, partial identification, and prediction under independently justified model restrictions.