Exact GH Equivalence of Fubini--Study and Fisher--Rao Metrics

This QBN mathematical preprint proves exact Gromov–Hausdorff equivalence between Fubini–Study quantum metric and Fisher–Rao classical information geometry under deficit gradient flow coarse-graining, with fixed scaling d_FR=2 d_FS. It establishes the complete bidirectional Chentsov–Fubini–Study correspondence linking unitary invariance (quantum) and Markov invariance (classical), unifying quantum and classical information geometry within the universal QBN metric framework.