发表机构
College of Computer Science; Software Engineering\ University, Nanjing, China（; ）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过复制程序与精确线性规划证书，将四个随机变量 Ingleton 分数的上界改进至 19/124，并验证了相关不等式目录的最优性。
AI 中文摘要
对于四个有限离散随机变量，我们证明 Ingleton 表达式的负值除以联合熵至多为 $19/124 \approx 0.15323$，将先前报道的上界 $3/19$ 改进了 $11/2356$。证明使用了一个包含四个复制步骤和六个辅助变量的复制程序，并通过精确的有理线性规划证书进行验证。我们还表明，Dougherty-Freiling-Zeger 和 Csirmaz 发表的两个信息不等式，通过显式的非负组合与 Shannon 不等式，蕴含了 $5/32$ 这一界，并且 $5/32$ 是此处考虑的三个已发表不等式目录的并集以及这些目录中出现的全部 213 个不同复制程序的完整复制引理扩展的精确最优值。新程序不在这类程序之列，且当所有这些程序和所有目录不等式被加入时，$19/124$ 这一界仍然是最优的。辅助文件提供了解析后的目录、精确的原始和对偶证书、精确的扩展证书，以及仅使用 Python 标准库的验证器。
英文摘要
For four finite discrete random variables, we prove that the negative of the Ingleton expression, divided by the joint entropy, is at most $19/124 \approx 0.15323$, improving the previously reported upper bound $3/19$ by $11/2356$. The proof uses a copy program with four copy steps and six auxiliary variables, certified by exact rational linear-programming certificates. We also show that two published information inequalities, due to Dougherty-Freiling-Zeger and Csirmaz, imply the bound $5/32$ by an explicit nonnegative combination with Shannon inequalities, and that $5/32$ is the exact optimum both of the union of the three published inequality catalogues considered here and of the full copy-lemma extensions of all 213 distinct copy programs occurring in them. The new program is not among these programs, and the bound $19/124$ remains optimal when all of them and all catalogue inequalities are added. Ancillary files provide the parsed catalogues, exact primal and dual certificates, exact extension certificates, and verifiers that use only the Python standard library.
Comments5 pages. Ancillary files contain the parsed inequality catalogues, exact rational certificates for the bounds 5/32 and 19/124, exact extension certificates for all 213 catalogued copy programs, and verifiers using only the Python standard library
