Recent advances in Large Language Models have fostered a new class of generative linguistic steganography, claim “provably secure” by theoretically aligning the steganographic distribution with the language model’s natural distribution. We challenge this premise by exposing Low-Probability Vanishing (LPV), an inevitable vulnerability arising from finite-precision arithmetic. To exploit this, we propose RRNs-HT, a novel steganalysis framework based on Representative Random Numbers and Hypothesis Testing, which transforms the detection task from semantic classification to a statistical audit of the sampling mechanism. Crucially, unlike previous work that contrasts machine text against human text, we validate our method in a rigorous homologous setting to strictly isolate sampling artifacts. Experiments demonstrate that RRNs-HT effectively breaks the security of AC and Meteor with high detection accuracy, whereas state-of-the-art semantic steganalyzers degrade to random guessing. Our findings prove that theoretical security is unattainable in practice without addressing finite-precision leakage.