We establish a hidden extension in the Adams spectral sequence converging to the stable homotopy groups of spheres at the prime 2 in the 54‐stem. This extension is exceptional in that the only proof we know proceeds via Pstragowski's category of synthetic spectra. This was the final unresolved hidden 2‐extension in the Adams spectral sequence through dimension 80. We hope this provides a concise demonstration of the computational leverage provided by ${\mathbb{F}}_2$‐synthetic spectra.

中文翻译：

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54维的Adams光谱序列的扩展

我们在Adams光谱序列中建立了一个隐藏的扩展，并收敛到54词干素数2的稳定球同伦群。这种扩展是个例外，因为我们知道的唯一证明是通过Pstragowski的合成光谱类别进行的。这是直到80维的Adams光谱序列中最后未解决的隐藏2扩展。${\mathbb{F}}_{\mathrm{2个}}$合成光谱。