Assuming the stable Hypothesis H, a degree-4 class lifting to stable cohomotopy in degree 4 must have cube divisible by 6, with 6 attained, making the M-theory Chern-Simons term integral without E8 gauge fields.
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Cohomotopy and flux quantization in $M$-theory
Assuming the stable Hypothesis H, a degree-4 class lifting to stable cohomotopy in degree 4 must have cube divisible by 6, with 6 attained, making the M-theory Chern-Simons term integral without E8 gauge fields.