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Mathematical analysis demonstrates sharp cancellation thresholds for quadratic remainder bounds, revealing that local zero isolation does not ensure global uniqueness.
A quadratic leading term with a remainder controlled relatively to its magnitude satisfies a sharp two-sided absolute-value bound. Below the exact cancellation threshold, a nonzero coefficient isolates the zero without a sign restriction on the coefficient. The note proves the threshold sharp and gives a polynomial example showing that local control does not imply global uniqueness.
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Ritsuki Kawada (2026) studied this question.
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