The Universal Coefficient 1.401 as a Critical Parameter in Quantum Gravity and String Compactification

We present a first-principles derivation of the fundamental coefficient 1.401, emerging atthe intersection of quantum field theory, Calabi-Yau geometry, and M-theory dynamics.Through three independent frameworks – (1) transfinite operator theory on complex man-ifolds, (2) p-adic regularization at the electroweak scale (p = 137), and (3) radion metricanalysis – we demonstrate this value’s universal role as a critical parameter governing phasetransitions between 4D QFT and 7D topological states. The convergence of these approachessuggests 1.401 may represent a new mathematical constant in quantum gravity.