Symbolic regression generates readable equations, but struggles to encode unit-sensitive thresholds and conditional logic. This paper proposes logistic-gated operators (LGOs), differentiable gates with learnable locations and steepnesses, which are embedded as typed primitives and mapped to physical units for auditing. On two major health datasets (ICU and NHANES), the hard-gate variant recovers clinically relevant cutoff points. Seventy-one percent (5/7) of the estimated thresholds fall within 10% of the guideline cutoff points, and 100% fall within 20%, using significantly fewer gates than the soft variant (ICU median 4.0 vs. 10.0; NHANES 5.0 vs. 12.5). Furthermore, it maintains an accuracy range competitive with that of the robust SR baseline. For primarily soft tasks, gates are truncated, preserving parsimony. Consequently, the resulting concise symbolic equations with explicit unit-sensitive thresholds are auditable against clinical cutoff points. This shifts interpretability from a posteriori explanations to modeling constraints, and provides practical computational methods for regime switching and governance-ready deployment in symbolic regression.