The Law of Thresholded Repair: A Universal Principle of Precision

We propose the Law of Thresholded Repair: precision in dynamic systems emerges whenrepairs are triggered only after a signal crosses calibrated thresholds with hysteresis.By delaying action until evidence is strong—and by requiring a distinct “return path”to clear the trigger—systems avoid chatter, reduce false positives, and maintainaccuracy under noisy measurements. We study thresholded control in simplified single- and multi-echelon environments withnoisy demand, shocks, drift, and oscillation. Event-triggered, hysteresis-basedinterventions maintain target performance with fewer corrections than continuous ornaïve reactive policies. Threshold width scales with noise variance; too narrow causesoscillation and overshoot, too wide causes delay and backlog. Ablations confirm eachcomponent’s role: removing thresholds induces chatter; removing hysteresis producesflip-flop behavior; removing noise-gating degrades precision. **Predictive claims (candidate, falsifiable)**• Thresholded + hysteresis control preserves service accuracy under noise while lowering intervention cadence. • Optimal thresholds increase with signal variance and desired confidence. • Under oscillatory regimes, hysteresis suppresses limit cycles compared to non-thresholded rules. • Excessive thresholds trade precision for delay; backlog rises in a predictable way. **How to falsify**Show a calibrated environment where thresholded, hysteresis-based repair cannot matchor beat a non-thresholded baseline on precision at comparable (or lower) interventionburden—or where removing hysteresis does not increase chatter/overshoot. All results are from research simulations in simplified settings and are intended asfalsifiable candidate predictions, accompanied by a reproducibility bundle (data,configs, and harness).