The nuclear fusion reaction can be catalyzed in a suitable fusion fuel by muons (heavy electrons).“For the fractal relations, ranging from DNA knots to solar neutrino flux signals”, ever derived of scale-invariant properties distinguished between classical invariant theory & quantum invariant theory subfactors. Accompanying isomorphicity & Connes FusionTensor Product retrieved to μ-catalyzed fusion where surroundings of room temperature fusion driven by the balance in mtDNA fusion & fission. On behalf of nanometer dimension of radius of heavy electron & wavelength of UV-light,it assumed that muons can be produced by oxidation-like decay when UV-light impinging water, indicated by a magnetic field induced perhaps by a ring South-North poled element.