标题： 通过混沌多维筛法和随机矩阵理论的启发式有界素数间隔 显示英文标题

标题： Heuristic Bounded Prime Gaps via a Chaotic Multidimensional Sieve and Random Matrix Theory

摘要： 我们提出增强的多维混沌启发筛（EMCHS），这是一种新颖的概率框架，结合混沌扰动和随机矩阵理论（RMT），以提出对素数间隔的改进界限。 基于Goldston-Pintz-Yildirim和Maynard的基础筛法，EMCHS在部分Elliott-Halberstam猜想（EHC）下delta = 0.3的条件下，提出了最多为180的无条件间隔和最多为8的条件间隔。 这些启发式建议通过细化的多面体优化和概率增强超越了Maynard的无条件界限246。 我们提供了某些分析组件的严格证明（例如通过遍历理论来界定混沌扰动），并明确区分哪些论点和结论是启发式的或假设性的。 针对10^18以内的素数的数值证据支持该框架，我们讨论了局限性和未来严格工作的方向。 显示英文摘要

摘要： We present the Enhanced Multidimensional Chaotic Heuristic Sieve (EMCHS), a novel probabilistic framework that integrates chaotic perturbations and random matrix theory (RMT) to suggest improved bounds on prime gaps. Building upon the foundational sieves of Goldston-Pintz-Yildirim and Maynard, EMCHS heuristically suggests unconditional gaps of at most 180 and conditional gaps of at most 8 under a partial Elliott-Halberstam conjecture (EHC) with delta = 0.3. These heuristic suggestions surpass Maynard's unconditional bound of 246 through refined polytope optimizations and probabilistic enhancements. We provide rigorous proofs for certain analytic components (such as bounding chaotic perturbations via ergodic theory) and explicitly distinguish which arguments and conclusions are heuristic or conjectural. Numerical evidence for primes up to 10^18 supports the framework, and we discuss limitations and avenues for future rigorous work.