Grey noise is white noise filtered through the inverse of the ISO 226 equal-loudness contour, producing sound that is perceived as equally loud at all frequencies. The human ear is not flat: it is most sensitive around 2-5 kHz (due to ear canal resonance) and less sensitive at low and very high frequencies. Grey noise compensates for this by boosting frequencies where we hear poorly and cutting where we hear best.
Most consumer "white noise" machines and apps actually produce something closer to grey noise without labeling it correctly. True white noise (flat spectral density) sounds harsh and bright. Grey noise sounds smooth and balanced. During Ebbi's development, we discovered this discrepancy and built both, accurately labeled, so users can choose based on what actually works for their brain.
No study has tested grey noise specifically for ADHD or cognition. It is included as a perceptual variant of white noise designed for comfortable extended listening. The ADHD benefit is inherited by analogy from the white noise evidence base.