Entanglement fingerprint of a non-invertible symmetry: exact Fibonacci cut charges on the lattice

Non-invertible defects are usually diagnosed through scaling spectra or infrared CFT data. We show that the Fibonacci duality defect of the critical golden chain already carries an exact categorical fingerprint at finite lattice size. The even-length antiferromagnetic ground state has fixed cut-charge weights, giving P_tau/P_1=phi^2 and log g=log phi without finite-size extrapolation. The proof is a finite-dimensional operator identity for the sandwiched cut projectors, combined with a Perron-Frobenius sector theorem for the even-length ground state. This gives a sharp lattice-level boundary entropy for a non-Abelian duality defect. We also separate this exact two-charge result from the finer six-primary tricritical-Ising resolution: the latter is located by the standard scaling-limit Virasoro branching of A_4 affine-TL packets, and is not an assumption in the finite-size theorem.