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We study a parametric deformation of the unified genus-1 anharmonic potentialand derive a parametric form of perturbative/non-perturbative (P/NP) relation,applicable across all parameter values. We explicitly demonstrate that theperturbative expansion around the perturbative saddle is sufficient to generateall the nonperturbative information in these systems. Our results confirm theknown results in the literature, where the cubic and quartic anharmonicpotentials are reproduced under extreme parameter values, and go beyond theseknown results by developing the nonperturbative function of real and complexinstantons solely from perturbative data.

Unified genus-1 potential and parametric P/NP relation