A Mathematical Model for Predicting Phase Transition and Structural Recovery Points in Threshold-Governed Systems

Key Points

• The aim is to develop a mathematical model to predict phase transition points in threshold-governed systems.
• Derived dynamic efficiency indices using a mathematical framework.
• Normalized time-derivative data to quantify deviations from ideal growth states.
• Monitored structural divergence between operational momentum and systemic resilience.
• Successfully predicted critical slowing down in threshold-governed systems.
• Identified key phase transition points using the model.
• Quantified improvements in understanding system resilience through geometric progression analysis.