What process was essential for Hubble to confirm a star in Andromeda was a true Cepheid variable, rather than noise or a foreground star?

Answer

Distinguishing the observed variation from the specific, consistent periodic cycle characteristic of a true Cepheid.

Hubble had to perform painstaking verification across multiple photographic plates over significant time spans to be certain that the observed flickering matched the specific, consistent periodic cycle of a true Cepheid variable, distinguishing it from random noise or observational error.

What process was essential for Hubble to confirm a star in Andromeda was a true Cepheid variable, rather than noise or a foreground star?
measurementHubblegalaxyDistanceCepheid