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Is there such a value as a negative Z or inverse Z related to the original Z value, which is the double SHA256 of the unsigned tx+01000000. I know there is a negative S value, is there a negative Z as well?

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The result of an SHA256 operation is a typically presented as a 32-byte array or slice or similar structure. 32 x 8 = 256. It can be presented in software as an unsigned integer. It would arguably be wrong to interpret it as a signed integer. It is usually displayed in any convenient encoding such as Hex.

Either way there is only one "solution" - there is not an alternative negative solution. It is not like a U-shaped curve such as y=x^2 providing two solutions for x, positive and negative, for any positive value of y. It is just not that sort of thing. Producing a single unambiguous result is a desirable feature of a hashing algorithm.

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