Counterexamples and controller corrections for full-state hybrid projective synchronization of discrete systems

This independent mathematical correction note examines the printed controllers and global synchronization claims in Adel Ouannas, “On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems,” Journal of Nonlinear Dynamics (2014), Article ID 983293, DOI: 10.1155/2014/983293. An exact Fold–Lorenz trajectory with geometrically diverging error refutes the forward assertion for the printed controller, including the example parameters and gains. An exact Lorenz–Lorenz stationary pair with nonzero error refutes the general inverse assertion. Corrected controllers recover the intended linear error dynamics and quantitative geometric convergence estimates under explicit existence assumptions. The note also gives an exact stability criterion for the printed forward controller and a counterexample to the rounded forward sufficient condition. These conclusions concern the published formulas and do not establish which controllers were used for the numerical figures. The record includes the final revised PDF, complete LaTeX source, and a Python script using standard-library exact rational arithmetic.