Tabular applications often require inspectable prediction rules and stable behavior when records are incomplete. We propose FlagGAM, a rule-basis framework that separates feature-level rule construction from prediction. A Flag Core Module converts numerical and categorical variables into sparse, human-readable univariate bases: threshold flags, category-level flags, tail-deviation bases, and categorical step functions. A default additive head combines these bases as a restricted GAM-style predictor, while the retained sparse rule-basis matrix supports mixed-type classification and regression, feature-specific weighting, and optional flexible heads. On clean benchmarks, additive FlagGAM stays close to modern additive and rule-based baselines on classification and improves over global linear modeling on regression, while remaining less flexible than tree-based predictors. Its clearest advantage appears under deployment-time perturbations: across three classification datasets, FlagGAM has the smallest mean AUROC degradation under missingness and numerical noise. Flexible heads improve absolute accuracy and approach strong tree-based baselines, but should be interpreted as nonlinear predictors over learned rule bases. These results support FlagGAM as a constrained additive rule-basis model for applications that need readable rules and stable behavior with incomplete inputs.

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