A new preprint on arXiv (abs/2605.13980, May 2026) presents an explicit, gate-level construction of reversible oracles that evaluate arbitrary polynomial Diophantine systems over bounded integer domains. The authors synthesize a garbage-free arithmetic circuit using in-place two's complement operations and a single recycled accumulator, proving spatial complexity q = O((n + d²) log₂ N) logical qubits and Toffoli depth O(q²). This is a preprint, not yet peer-reviewed; validation rests on analytical derivations plus small-scale circuit simulations rather than large statistical samples. The work directly addresses the gap between Hilbert's tenth problem (undecidable in the unbounded case) and practical quantum advantage by restricting to finite intervals, thereby admitting quadratic speedup via amplitude amplification. Classical exhaustive search scales as O(N^n); the quantum routine achieves the expected Grover square-root improvement with only polynomial overhead in the arithmetic synthesis. Related literature includes Grover's 1996 search algorithm and later analyses of quantum arithmetic cost (e.g., Gidney & Ekerå 2021 on modular multiplication). The paper's key advance is showing that the non-Clifford depth remains independent of variable count once coefficient Hamming weights are fixed, a structural property missed by abstract oracle models. Limitations include the bounded-domain restriction and the assumption of fault-tolerant logical qubits; no hardware implementation or noise analysis is provided. Connections to cryptography follow naturally: many integer-relation problems in lattice-based schemes are precisely bounded Diophantine instances, suggesting a concrete route for quantum-assisted cryptanalysis once scalable hardware arrives.