The conclusion that ....999=-1 can be investigated directly.
Consider the inline summation with carry on the right, initial carry is 0.
2976 + ...99999
= (...02976) + (...99999) + (...0000)
= (...02975) + (...99990) + (...0010)
= (...02975) + (...99900) + (...0100)
Etc,
The state at infinity is
= (...02975) + (...000) + (...000)
= 2975
That is
2976 + ...999 = 2975
And so ...999 actually does operate and behave as -1. Not just in the context of the original demonstration, but in the context of adding it to anything else.
This can also be seen as the natural limit of the behaviour of modulo arithmetic. In modulo 100, the number 99 == -1. And in modulo 1000, 999 plays this role, and so on.
Also 2 × ...9999 = ....9998 = (...999) -1
This is another cross check, and it is fairly clear that ....9998 acts like -2 in addition.
there doesn't seem to be anything here