This paper presents a novel event-triggered (ET) output-feedback optimal tracking control scheme for uncertain discrete-time pure-feedback nonlinear systems with immeasurable states. The key contributions include: 1. **Neural State Observer Design**: A neural network (NN) is designed to estimate the immeasurable system states in real time, decoupling the observer and controller design. The observer NN weights are updated using a specific law to ensure uniform ultimately bounded (UUB) behavior. 2. **Event-Triggered Mechanism**: An ET condition is developed to reduce network burden and save network resources. The controller is only activated when the ET condition is satisfied, reducing the number of transmission events. 3. **Optimal Tracking Controller Design**: An optimal tracking controller is designed using an adaptive critic design (ACD) framework. The critic NN minimizes the long-term performance measure, while the action NN updates the control input to achieve optimal tracking. The variable substitution approach is used to handle nonaffine terms and avoid n-step time delays. 4. **Stability Analysis**: The closed-loop system signals are guaranteed to be UUB, ensuring stable tracking performance. The ET condition is designed to balance network resource savings and tracking accuracy. 5. **Simulation Results**: Simulations demonstrate the effectiveness of the proposed control scheme, showing that the system output tracks the desired reference signal, the tracking error converges to a small neighborhood, and the controller reduces network transmission events by approximately 48.8%. This work addresses the challenges of control design for discrete-time pure-feedback nonlinear systems with immeasurable states, providing a robust and efficient solution for optimal tracking control.This paper presents a novel event-triggered (ET) output-feedback optimal tracking control scheme for uncertain discrete-time pure-feedback nonlinear systems with immeasurable states. The key contributions include: 1. **Neural State Observer Design**: A neural network (NN) is designed to estimate the immeasurable system states in real time, decoupling the observer and controller design. The observer NN weights are updated using a specific law to ensure uniform ultimately bounded (UUB) behavior. 2. **Event-Triggered Mechanism**: An ET condition is developed to reduce network burden and save network resources. The controller is only activated when the ET condition is satisfied, reducing the number of transmission events. 3. **Optimal Tracking Controller Design**: An optimal tracking controller is designed using an adaptive critic design (ACD) framework. The critic NN minimizes the long-term performance measure, while the action NN updates the control input to achieve optimal tracking. The variable substitution approach is used to handle nonaffine terms and avoid n-step time delays. 4. **Stability Analysis**: The closed-loop system signals are guaranteed to be UUB, ensuring stable tracking performance. The ET condition is designed to balance network resource savings and tracking accuracy. 5. **Simulation Results**: Simulations demonstrate the effectiveness of the proposed control scheme, showing that the system output tracks the desired reference signal, the tracking error converges to a small neighborhood, and the controller reduces network transmission events by approximately 48.8%. This work addresses the challenges of control design for discrete-time pure-feedback nonlinear systems with immeasurable states, providing a robust and efficient solution for optimal tracking control.