We introduce a deterministic sparse Fourier transform framework based on a keyed multi-view gating mechanism that leverages 2-of-3 Chinese Remainder Theorem (CRT) agreement to reduce candidate frequency pairs from $O(k^2)$ to $Θ(k)$ under sparse-regime assumptions. Unlike prior approaches that rely on randomized bucketization for candidate formation, the proposed method provides deterministic structure with probabilistic guarantees arising only from assumptions on frequency placement and independence of affine hashing across views. The algorithm is realized through a peeling-based recovery procedure that extracts frequencies directly from singleton bins without explicit pair enumeration. A recursive self-reduction eliminates the $O(\sqrt{N} \log N)$ preprocessing floor, yielding $O(\sqrt{N} \log k)$ expected identification time while maintaining an $O(N \log N)$ worst-case bound via deterministic dense-FFT fallback. A multi-view verification framework combining Parseval energy consistency and bin-wise residual checks ensures bounded failure probability and no false negatives under correct verification. This establishes a framework combining deterministic candidate reduction, sublinear expected complexity, and worst-case safety guarantees within a CRT-based sparse FFT architecture.

翻译：我们提出了一种基于键控多视角门控机制的确定性稀疏傅里叶变换框架，该机制利用“三取二”中国剩余定理（CRT）一致性约束，在稀疏假设下将候选频率对从 $O(k^2)$ 缩减至 $\Theta(k)$。与依赖随机桶划分进行候选生成的现有方法不同，所提方法提供确定性结构，其概率保障仅源自对频率位置假设以及各视角间仿射哈希独立性的假设。该算法通过基于剥离的恢复过程实现，直接通过单例桶提取频率，无需显式列举候选对。递归自约简消除了 $O(\sqrt{N} \log N)$ 的预处理底层开销，从而实现 $O(\sqrt{N} \log k)$ 的期望识别时间，同时通过确定性密集FFT回退机制保持最坏情况下的 $O(N \log N)$ 复杂度。结合Parseval能量一致性与桶级残差校验的多视角验证框架，确保在验证正确的情况下，失败概率有界且无漏检。该框架在中国剩余定理的稀疏FFT架构中，实现了确定性候选缩减、亚线性期望复杂度与最坏情况安全保证的统一。