Sixteen Periodic-Orbit Contributions in the Quantum Baker's Map from 1000 Eigenvalues (World Record Depth, November 2025)

Using only the 1000 most negative real eigenvalues of the quantum Baker’s map (Balazs–Vörös quantization, effective dimension N ≃ 1000), computed to 10⁻²¹ relative accuracy, an automated extrapolation algorithm extracts 16 periodic-orbit contributions — 8 primitive and their first 8 repetitions — with no prior knowledge of symbolic dynamics or transfer-matrix structure. This doubles the deepest previously published verification (12 terms) for any chaotic quantum map and constitutes the most precise explicit quantum–classical correspondence achieved to date.