After an automatic brake application, what does actuating with the independent brake valve signal?

Actuating with the independent brake valve after an automatic brake application indeed signals the nullification of the signal to the J-Relay from the control valve. This is crucial because the J-Relay is responsible for allowing the air brake system to function properly, particularly in managing the application and release of brakes during a train's operation. By nullifying the signal to the J-Relay, the operator effectively takes control of the braking system, which allows for a more nuanced management of brake pressure following an automatic application. This allows for better handling of situations where an immediate response is required, without automatically reverting to the conditions dictated by the control valve and existing automatic applications.

This action doesn't instantly release the brakes, apply them harder, or activate emergency brakes, but rather allows for specific control over the brake system in a way that optimizes safety and operational efficiency.