AI 中文总结
研究位置空间中四点共形积分，利用主导奇点等建立自举工作流程，适用于三圈情况，在四圈情况中通过积分分解得到难以计算的积分，还提供适合人工智能模型的文件包。
AI 中文摘要
我们建立了一个自举工作流程来研究位置空间中的四点共形积分，使用主导奇点、单值多重对数假设和区域展开的边界数据。这些四点共形积分具有一般性，由所有可能的$f$-图的四点投影生成，包括所有非平面$f$-图扇区。对于三圈情况，十五个不等价被积函数基中的十四个可通过\texttt{HyperlogProcedures}直接计算，最后一个由格拉姆恒等式确定。接着研究自举工作流程在四圈情况中的适用性，通过将具有多个主导奇点的积分分解为具有更简单切割结构的部分使其易于处理，得到了一些目前其他方法难以计算的四圈积分，还提供了适合当前人工智能模型读取和使用的技能文件包。
英文摘要
We set up a bootstrap workflow to study four-point conformal integrals in position space, using leading singularities, single-valued multiple polylogarithmic ansätze and boundary data from expansion by regions. These four-point conformal integrals are general in the sense that they are generated by the four-point projections of all possible $f$-graphs, including all non-planar $f$-graph sectors. For three-loop cases, fourteen of the fifteen inequivalent integrand basis can be directly calculated by \texttt{HyperlogProcedures} and the last one is fixed by Gram identity. Then we concentrate on how far the bootstrap workflow can go for four-loop cases, though it works for three-loop cases as well. We show that integrals with several leading singularities can be made tractable by decomposing them into pieces with simpler cut structure. Some four-loop integrals which can not be calculated or very hard to be calculated by other methods for now are obtained in this way. We also provide a package with skill files which is suitable to be read and used by current AI models.
Comments32 pages, 9 figures. citation corrected
