AI 中文总结
本文提出一种计算机辅助方法，利用不稳定莱布尼茨法则和EHP序列自然性计算不稳定Adams谱序列微分，给出球面2-主不稳定同伦群至50-茎的阶数界及证明示例。
AI 中文摘要
我们提出了一种基于计算机的方法，通过系统地应用不稳定莱布尼茨法则以及相对于EHP序列中映射的自然性，来计算不稳定Adams谱序列中的微分。我们将结果记录在关于球面2-主不稳定同伦群阶数的上下界表格中，范围覆盖至不稳定50-茎。我们提供了若干微分的证明示例，并给出了解读相关不稳定Adams图表和用于微分证明的流程图表的指南。
英文摘要
We present a computer-based approach to computing differentials in the unstable Adams spectral sequence by systematically applying the unstable Leibniz rule and naturality with respect to maps in the EHP sequence. We record our results in tables of upper and lower bounds on the orders of 2-primary unstable homotopy groups of spheres through the unstable 50-stem. We provide examples of proofs for several differentials and give a guide to interpreting the associated unstable Adams charts and flow chart diagrams for differential proofs.
Comments(10 figures = 6 in the body + 4 legend panels; 5 tables = contradiction table + 4 bounds tables): 20 pages, 10 figures, 5 tables. Code and data at https://github.com/jfbaer/adams-ehp (doi:10.5281/zenodo.22820890); interactive Adams charts at https://jfbaer.github.io/adams-ehp/
