A counterexample and a controller correction for global synchronization of the fractional Newton–Leipnik reaction–diffusion system

This independent technical note examines the controller printed in equation (26) and the global synchronization assertion of Theorem 5.3 in Mansouri, Bendoukha, Abdelmalek and Youkana, Applicable Analysis 100 (2021), 675–694, DOI: 10.1080/00036811.2019.1616694. An incorrect product expansion leaves a quadratic term in the synchronization error equation. An exact spatially constant master–slave pair has nonzero stationary error, providing a counterexample under the published assumptions for every common Caputo order in (0,1] and every positive choice of diffusion coefficients. Replacing one product in the second controller restores cancellation. The revised note proves an explicit L² Mittag–Leffler error estimate under stated Hilbert-space regularity assumptions, using a self-contained quadratic memory identity and pointwise Caputo comparison. Synchronization is conditional on globally existing trajectories. The counterexample does not disprove local synchronization at a=0.4 and does not determine which controller was used in the original numerical code. The record contains the final revised PDF and editable TeX source archive, including exact rational Python verification. This is an independent correction note, not a journal-issued erratum. AI assistance is disclosed in the manuscript.