Abstract This study proposes the Convergence Pointas a novel variable governing the response behavior of large language models (LLMs). A Convergence Point refers to whether a given utterance contains a clear answer or logical endpoint toward which the model can converge — a variable independent of utterance length, complexity, or reasoning demand. The central claim of this study is as follows: what AI struggles with is not complex computation, but questions that humanity has yet to resolve. The source of this difficulty lies not in the model's training volume, but in the consensus structure of human knowledge systems. Using four small-scale language models (approximately 8B parameters) running in a local inference environment (LM Studio 0. 4. 6), we conducted first-utterance experiments across 13 categories and sequential utterance experiments across 12 categories. Beyond behavioral observation, we directly measured internal entropy at the prompt processing stage — prior to response generation — using the logitsₐll=True option in llama-cpp-python. Utterances with clear Convergence Points exhibited low internal uncertainty, while those structurally lacking a Convergence Point exhibited high uncertainty. In the fourth experiment, which varied only the degree of human knowledge consensus across three levels using a single subject (black holes), all three models showed a stepwise entropy increase in the order of 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. The fifth experiment confirmed that even under conditions where RLHF forced output convergence (self / consciousness), internal entropy did not converge. RLHF did not create a Convergence Point — it merely overlaid the absence of one at the output level. This study presents four layers of evidence — behavioral observation, internal entropy measurement, direct consensus-level verification, and RLHF forced-convergence verification — to argue that the limitations of AI may stem not from insufficient training within the model, but from the unresolved structure of human knowledge systems themselves. The Convergence Point can function not only as an explanatory variable for AI response behavior, but as an empirical criterion for determining where AI must defer to human judgment.
J.-H. Park (2026) studied this question.