How is positive feedback coupled to the input in a Pierce oscillator?

A Pierce oscillator is a type of crystal oscillator commonly used in digital circuits and amateur radio for highly stable frequency generation. It typically employs a single active device, such as a transistor or CMOS inverter, with a quartz crystal placed between the output and the input. The feedback network in a Pierce oscillator relies on an internal capacitive voltage divider, which is formed by the stray or explicitly added capacitors in the circuit. The crystal acts as an inductor in the resonant circuit, and positive feedback is provided via these capacitive paths back to the input to sustain oscillation. Other methods mentioned in the distractors belong to different circuits. For example, a tapped coil is the hallmark of a Hartley oscillator. Neutralizing capacitors are used to prevent unwanted oscillation in amplifiers, not to create the required positive feedback in an oscillator.