Researchers have discovered a method to identify non-invertible symmetries in quantum systems using a categorical fingerprint at finite lattice size. Specifically, the Fibonacci duality defect of the critical golden chain exhibits fixed cut-charge weights in the even-length antiferromagnetic ground state, yielding a precise ratio of P_tau/P_1=phi^2 and log g=log phi without requiring finite-size extrapolation1. This breakthrough allows for the exact calculation of certain quantum properties, such as the golden ratio phi, which is a fundamental constant in mathematics. The findings demonstrate that non-invertible defects can be diagnosed using exact methods, rather than relying on scaling spectra or infrared CFT data. This matters to practitioners because it provides a new tool for analyzing quantum systems with non-invertible symmetries, enabling more accurate predictions and a deeper understanding of their behavior.