We construct an unbounded representative for the shriek class associated to embeddings of spheres into Euclidean space. equip this $KK$-cycle with a connection and compute Kasparov product Dirac operator on $\\mathbb{R}^{n+1}$. find that resulting spectral triple algebra $C(\\mathbb{S}^n)$ differs from round sphere by so-called index cycle, whose in $KK_0(\\mathbb{C},\\mathbb{C})$ represents mu...