A homotopy-theoretic context for CKM/Birkhoff renormalization

We propose a geometric object slightly subtler than a complex line bundle with connection, a two-sphere fibration with structure group ${\mathrm{\Omega }}_e^2{S}^2$, to parametrize a space of dimensional regularizations in the metaphysics of renormalization theory. Comments, corrections, advice and suggestions are very welcome. To be continued.