标题： 不平衡素数筛：每个素数间隔都是莫比乌斯不平衡障碍的结果 显示英文标题

标题： Imbalance Prime Sieving: Every Prime Gap Is a Result of a Möbius Imbalance Obstruction

摘要： 我们引入了一种基于在莫比乌斯变换的有理度量空间中检测拓扑障碍的新素数筛法。 与依赖于可除性的传统筛法不同，我们的方法将素数识别为那些贡献新的、不冲突的不平衡共轭的数。 这提供了一种精确的素数枚举算法，并对素数间隔提供了新的几何解释。 该筛法在有理对 (p, q) 上构建了一个拓扑障碍理论，从中我们观察到每个素数间隔都是这个变换后的不平衡空间中碰撞的结果。 我们的实验结果表明，这种方法可以精确地过滤出指定范围内的素数，具有对新数论模型和筛法算法的潜在影响。 显示英文摘要

摘要： We introduce a novel sieve for prime numbers based on detecting topological obstructions in a M\"obius-transformed rational metric space. Unlike traditional sieves which rely on divisibility, our method identifies primes as those numbers which contribute new, non-colliding imbalance conjugates. This provides both an exact algorithm for prime enumeration and a new geometric interpretation of prime gaps. This sieve constructs a topological obstruction theory over rational pairs (p, q), from which we observe that every prime gap is a consequence of a collision in this transformed imbalance space. Our empirical results demonstrate that this method precisely filters the prime numbers up to a specified bound, with potential implications for new number-theoretic models and sieving algorithms.