arXiv:2611.06973v1 Announce Type: new Abstract: In this paper, we provide an upper bound on the number of a special system of Roth-type Diophantine inequalities over proper adelic curves. By refining the technique from previous work, we successfully eliminate the large-height restriction on the solutions. Furthermore, the constraints on the parameters within the inequality are further relaxed. We also give a constructive quantitative generalization of the Vojta-Dolce-Zucconi system, replacing compactness-based extraction by a discrete pigeonhole argument and a finite grid partition, so that the resulting bound has explicit dependence on the relevant parameters.
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