On the convergence estimates and objective-value reporting in a stochastic three-term conjugate gradient method

This technical note examines specific convergence arguments and numerical reporting in Liu, Yuan, and Tang, Electronic Research Archive 34(10) (2026), 7201–7221, DOI: 10.3934/era.2026311. It derives the correct geometric-series bound from the recurrence in Theorem 1, explains why Theorem 2 does not imply exact stationarity for fixed positive gradient-noise variance, and identifies an incompatibility between nonnegative defined losses and negative plotted objective values unless an unreported transformation was used. The note does not claim a counterexample to Theorem 1 for actual TSTCG trajectories or a general disproof of the algorithm. The package contains the PDF, LaTeX source, and exact-arithmetic verification script. AI assistance and responsibility: OpenAI ChatGPT was used for English improvement, auxiliary computational checks, and assistance with mathematical analysis. All mathematical statements, counterexamples, lemmas, theorems, proofs, interpretations, and the final text remain the responsibility of the author.