When Should a Productivity App Step In? We Ran the Numbers

Nine thresholds, one decision, and the math that settled it

This is the technical deep dive into the stopping rule formula from yesterday’s article on the mathematical systems I created to address overworking. Here’s how we built the 0.3 threshold into Asaura AI and the decisions involved in getting the system to respond without being overly aggressive.

The stopping rule formula is P × C > 0.3. But why 0.3? Why not 0.5? Why not 0.1?

This threshold determines how aggressive the system is about deepening tasks. Higher thresholds mean more tolerance for friction. Lower thresholds mean faster intervention.

We tested nine thresholds. Here’s what each one revealed.