Yes, Sunlight Soap was originally guaranteed to be pure, genuine, and free from adulteration.
While the exact composition of Sunlight Soap may have changed over time, when it was first created in 1884, Lever Brothers (now Unilever) promised its purity. Pental Products, which also manufactures Sunlight soap, states that strict quality controls ensure Sunlight maintains a high quality standard. This suggests a commitment to a certain level of purity and quality, though the exact definition of "pure" might vary by modern standards.
