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The authors propose an online low-rank tensor estimation method based on stochastic gradient descent that processes observations sequentially without storing historical data, overcoming the memory and scalability limitations of traditional offline approaches. Beyond estimation, the paper introduces a novel online debiasing technique that delivers valid confidence intervals and hypothesis tests on the fly without data splitting. Theoretical results establish near-minimax-optimal convergence rates and asymptotic normality for general linear functionals of tensors. 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