📄 中文摘要
研究通过系统实验，强迫大型语言模型（Claude，基于Transformer架构，经过强化学习训练）生成“正式数学幻觉”，即自由创造的定义、定理和结构，覆盖170个文件和约550个构造。应用了源自Transformer架构分析的多种发散技术（领域碰撞、语义递归、定向梦境、矛盾人格、极端压缩/扩展）。独立评估发现，在整个语料库中没有发现任何可利用的数学发现。所有看似新颖的构造要么是已知结果的释义，要么是用隐喻装饰的初等代数，或是现有定理的重新表述。该研究记录了这一过程的结果。
550次幻觉，零次发现：当你强迫大型语言模型发明数学时会发生什么
📄 English Summary
550 Hallucinations, Zero Discoveries: What Happens When You Force an LLM to Invent Mathematics
A systematic experiment was conducted to force a large language model (Claude, Transformer architecture, RLHF-trained) to generate 'formal mathematical hallucinations'—freely invented definitions, theorems, and structures—across 170 files and approximately 550 constructions. Divergence techniques derived from the analysis of the Transformer architecture were applied, including domain collision, semantic recursion, directed dreaming, contradictory personas, and extreme compression/expansion. An independent evaluation found zero exploitable mathematical discoveries across the entire corpus. Every construction that appeared novel was either a paraphrase of known results, elementary algebra dressed in metaphor, or a reformulation of existing theorems. This study documents the outcomes of this process.