Abstract This study proposes the Convergence Point as a novel variable governing the response behavior of language models. A Convergence Point refers to whether a clear answer or logical terminus exists within an utterance toward which an AI can converge — a variable independent of utterance length, complexity, and reasoning demand. The central claim of this study is as follows: what AI struggles with is not complex computation, but questions on which humanity has yet to reach consensus. The cause lies not in the model's internal volume of training data, but in the consensus structure of the human knowledge system. Four small language models (8B parameter scale) running in a local inference environment (LM Studio 0. 4. 6) were tested across a first-utterance experiment covering 13 categories and a sequential-utterance experiment covering 12 categories. Going beyond behavioral observation, internal entropy was directly measured at the prompt-processing stage prior to response generation, using the logitsₐll=True option in llama-cpp-python. Utterances with a clear Convergence Point exhibited low internal uncertainty, while utterances structurally lacking a Convergence Point exhibited high uncertainty. In the fourth experiment — in which a single subject (black holes) was held constant while the degree of human knowledge consensus was varied across three levels — all three models showed a stepwise ascending entropy pattern in the order: full consensus → partial consensus → no consensus. This constitutes the first direct evidence that the degree of human knowledge consensus is directly proportional to prompt-level input entropy. In the fifth experiment, it was confirmed that even under conditions where output was forcibly converged through RLHF (self/consciousness), internal entropy did not converge. RLHF did not create a Convergence Point; rather, it suppressed at the output level the absence of any Convergence Point. Through four layers of evidence — behavioral observation, internal entropy measurement, direct verification of consensus level, and RLHF forced-convergence verification — this study proposes that AI's limitations may originate not from the model's internal volume of training, but from the unresolved structure of the human knowledge system itself. The Convergence Point can function not only as an explanatory variable for AI response behavior, but as an empirical criterion for determining the points at which AI must defer to human judgment.
J.-H. Park (Thu,) studied this question.