Generative Mathematical Physics G: Dynamical Equivalence of G2 Singularity Resolution and Loop Quantum Cosmology Bounce

This paper establishes a rigorous mathematical isomorphism between the singularity resolution process on G2 manifolds and the quantum bounce mechanismin Loop Quantum Cosmology (LQC). By constructing a correspondence betweenthe metric evolution equation for singularity resolution and the effective dynamics of LQC, we prove that both share the same algebraic structure of generators.Specifically, we demonstrate that the Kähler resolution of ADE singularities on G2manifolds, in an appropriate limit, is equivalent to the bounce dynamics in theeffective Friedmann equation of LQC, where the resolution parameter correspondsto the critical density in LQC, and the intersection form of exceptional divisors corresponds to the power-law structure of quantum geometric corrections. Throughthe McKay correspondence, different ADE singularity types (Ak, Dk, E6, E7, E8)are put into one-to-one correspondence with the correction exponent α = 1,3/2,2of LQC. This isomorphism provides a unified mathematical framework for understanding singularity avoidance in quantum gravity and yields numerically testablecorrection formulas. A numerical simulation scheme is proposed: by constructinga two-dimensional discrete Kähler model, one can extract the geometric evolutionexponent and compare it with the LQC bounce exponent.