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When raising pitch the NSL tension is at the top of the Tension Band. WE KNOW that.

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There is no standard terminology. Just replace your own terminology in your own head when you read mine. Thank you.

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This range narrows and rises on hard blows.

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That's the Tension Band, and given the same string and friction conditions, it will always have the same width.

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I don't know how many more ways I can explain it to you. You seem like an intelligent person. Please take this as a honest concern, but I think there maybe something else going on that is getting in the way of you being able to see how this simple concept works.

I'll give you one example.

First the background.

NSL tension sensitivity depends on two things: the length of the NSL and the tightness of the pin block.

The longer the NSL, the less sensitive the tension is to pin movement.

The tighter the pin block, the more the pin moves, and the more the NSL tension changes during tuning and after the hammer force is removed.

Let's consider raising pitch with slow pull, on a large grand with not so tight pins, hammer at 12:00.

When raising pitch the NSL tension is at the top of the Tension Band. WE KNOW that.

When we arrive at the target pitch and remove the hammer force, the pin unbends to the left, perpendicular to the string; no change in NSL tension.

The pin untwists counter-clockwise. This lowers NSL tension. But because the pin block is not so tight, and the NSL tension is long, we KNOW the NSL tension does not lower very much at all.

This is a rare situation where the pitch may actually rise on hard blows because the NSL tension is left so high in the Tension Band.

I have proven these hypotheses and you can too. Just slow pull a string to any pitch, take note of the pin tightness and NSL length, measure the pitch, do a test blow, measure again.

If you change the hammer angle, you should be able to predict the resulting change in stability.

I.e. in the example above, if the pitch does rise, a change in angle from 12:00 to 3:00 will add unbending toward the string when the hammer force is removed. This leaves the NSL tension lower in the Tension Band, which may be enough to stop the pitch from rising.

All of this is pure speculation. The tension at any given point on the string should depend on the friction between the various sections of the string, and what the tension was in the various areas before the string gets to its final tension. If the difference between different sections of the string is small, the friction may be enough to keep the string stable even if there is a difference in the tension. This is how looped strings stay in tune on adjacent notes, even though there may be different tensions on them.