Notes. ^(a)“Architectural guarantee” means the decision pathway is provably confined to the named concepts; unconstrained classifiers may exploit features through interactions that are not locatable on the concept layer even when SHAP values are inspectable. ^(b)Forward intervention: An expert assigns a corrected value to a named concept and reads the updated class posterior in a single forward pass, rather than perturbing an input and reattributing. ^(c)Nontrivial recovery: Because g ≠ id, replacing all learned concepts with ground truth does not reconstruct the raw input, so recovery rate is a genuine measurement of how far the learned representation has diverged from physical values (Sect. 4.3).