You seem to be concerned with the mathematics of the curve. But it's really important to remember that economics (and finance) is not a science like chemistry. Baking soda mixed with vinegar is not always a volcano, no matter how much of each ingredient is mixed.
The "yield curve" has virtually nothing to do with the curve. It has nothing to do with standard deviations. The issue is that the market is sending a very pessimistic message when it floods resources in to longer term debt to the point that it's priced higher than short term debt.
A central tenant of economics is growth. The population of humans expands, markets expand, new products are invented, etc. There's a general assumption that inflation will be positive, the buying power of $100 will diminish over time. All of this means that more time equals more risk which should equal more return. When the "yield curve inverts" the market is saying, "I'd rather lock in to 2% over 10-years now, even though I know my return in the near term will be less than I could get in shorter term instruments, because in 3-years I think it will be even lower and I'll be beating the market at that point." It's saying "I think the risk of time is backwards right now."
But there is no chemistry-like economics formula that says 2-parts of inverted yield curve mixed with 1-part average wage increase equals recession. There certainly isn't one that includes how wide the 2/10 year spread is. It's possible that an inverted yield curve means absolutely nothing. It might just mean that there is glut of 2-year debt available right now.
It's kind of like predicting an earthquake. There are sensors placed all over the planet, hundreds of millions of dollars of grant money employing thousands of people to study earthquakes. Very smart people can describe in painstaking detail why earthquakes happen. Super computers crunching mountains of data to find causation patters. And, zero people can tell you when an earthquake will happen.
Since I find visuals to be helpful here are yield curve charts.