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Hi Rich, I am not "the" expert.  Just sharing my observations and therefore subject to error and inaccuracies as well.

One thing I did do to satisfy my understanding of the feathering being Gaussian (or as is often called a Normal Curve),  I created a Black to White edge with a 10 pixel feather and plotted the black to white transition curve and plotted that against a cumulative Normal Curve.  It was a real close match confirming my understanding.

Here is the link to a Normal/Gaussian curve, the math, and what the CDF or Cumulative Distribution Function or the Normal curve: https://en.wikipedia.org/wiki/Normal_distribution

Following is the Graph of the CDF curve with a sigma of 10 vs the black to white 10 pixel feather transition in PS.  This is only to satisfy those such as Tony Bowman and myself where math gives comfort

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