AI 中文总结
通过引入两个独立分子指数并特化参数，改进了π的无理性度量上界至7.101862832357，较原界降低约0.0189%，并证明该参数点为局部极小值。
AI 中文摘要
我们在Zeilberger--Zudilin积分中引入两个独立的分子指数，并将其特化为\\[ A_1=A_2=\frac{1857}{2785}. \\] 由此得到的关于$1$和$\pi$的整数线性形式证明了\\[ \mu(\pi)<7.101862832357. \\] 这将Zeilberger--Zudilin上界$7.103205334137\ldots$降低了超过$0.001342501780$；未取整的界之间的差为$0.0013425017806509\ldots$，约为$0.01890\\%$。同一参数点在其允许的算术室中是显式辅助上界函数的严格二维局部极小值点。这是关于该函数的局部陈述，并非声称该点是所有构造中的全局最优解。
英文摘要
We introduce two independent numerator exponents into the Zeilberger--Zudilin integral and specialize them to \[ A_1=A_2=\frac{1857}{2785}. \] The resulting integer linear forms in $1$ and $π$ prove \[ μ(π)<7.101862832357. \] This lowers the Zeilberger--Zudilin upper bound $7.103205334137\ldots$ by more than $0.001342501780$; the difference between the unrounded bounds is $0.0013425017806509\ldots$, approximately $0.01890\%$. The same parameter point is a strict two-dimensional local minimizer of the explicit auxiliary upper-bound function in its admissible arithmetic chamber. This is a local statement about that function, not a claim that the point is a global optimizer among all constructions.
