What *exactly* is Clarity?

[ThomasT]

Hi,

camera raw and lightroom have the slider clarity.

But what exactly is clarity?
Yes I know what it is in principle, its mide ton contrast, but I'm asking for the algorithm to reproduce it in PS.
In the internet you read a lot about its like unsharp mask with large radius and small intensity. But this is true only for small corrections.
When moving the clarity-slider to the extrem right the image looks different. At first it seems that it influences only the luminosity.

But using an upper layer, applying unsharp mask (radius around 100, amount 20% -30%) and combining it with luminance-method looks quite differently.

I tried differenz things. Some come near, but not exaclty. And all what I found in the internet is rubbish and ad hoc thinking.

I need the hard slightly desaturated look when pushing clarity to the extreme.

[Paper_Mine]

I prefer Dehaze than Clarity to avoid photos look like over-sharpened.