标题： PFCS：用于确定性数据关系发现的素因数缓存系统 显示英文标题

标题： PFCS: Prime Factorization Cache System for Deterministic Data Relationship Discovery

摘要： 缓存系统由于无法精确捕捉数据关系，从根本上限制了现代计算性能。 尽管达到85-92%的命中率，传统系统依赖于统计启发式方法，无法保证关系发现，导致预取效果不佳和资源浪费。 我们提出了PFCS（质因数分解缓存系统），利用质因数分解的数学唯一性，实现无误报的确定性关系发现。 PFCS为数据元素分配唯一的质数，并将关系表示为合数，通过分解可以恢复完美的关系。 在数据库、机器学习和高性能计算工作负载上的全面评估表明，与最先进的系统相比，平均性能提高了x 6.2倍，命中率为98.9%，功耗降低了38%。 数学基础提供了近似方法无法实现的形式化保证，确立了缓存系统设计的新范式。 显示英文摘要

摘要： Cache systems fundamentally limit modern computing performance due to their inability to precisely capture data relationships. While achieving 85-92% hit rates, traditional systems rely on statistical heuristics that cannot guarantee relationship discovery, leading to suboptimal prefetching and resource waste. We present PFCS (Prime Factorization Cache System), which leverages the mathematical uniqueness of prime factorization to achieve deterministic relationship discovery with zero false positives. PFCS assigns unique primes to data elements and represents relationships as composite numbers, enabling the recovery of perfect relationships through factorization. A comprehensive evaluation across database, ML, and HPC workloads demonstrates an average performance improvement of x 6.2, 98.9% hit rates, and a 38% power reduction compared to state-of-the-art systems. The mathematical foundation provides formal guarantees impossible with approximation-based approaches, establishing a new paradigm for cache system design