A Hybrid Adaptive Mathematical Model for the Dynamic Proof of P = NP Equality

This paper proposes a hybrid adaptive mathematical model that extends beyond traditional computational complexity analysis to argue for the equality between the P and NP complexity classes. By utilizing Dynamic Integration and Negative Exponential Decay, the model demonstrates that the apparent gap between exponential growth: O(2^n) and polynomial time:O(n^k) can be collapsed. This framework suggests that, under conditions of optimal algorithmic compression and adaptive scaling, every NP problem possesses a core polynomial structure, thereby concluding that: P = NP within a dynamic computational system.