AI 中文总结
研究零场 Sherrington-Kirkpatrick 模型在零温度下的完全复制对称破缺，通过证明帕里西极小值性质及支撑集情况，以及β>1时帕里西测度支撑集情况，表明β→∞时q_β收敛到 1。
AI 中文摘要
我们证明了零场 Sherrington-Kirkpatrick 模型在零温度下的完全复制对称破缺：帕里西极小值是绝对连续的，具有光滑密度，支撑集为[0,1)。在逆温度β>1时，[arxiv.org/abs/2607.11756v3]证明帕里西测度支撑集为[0,q_β]。这里我们表明当β→∞时，q_β收敛到 1。
英文摘要
We prove full replica symmetry breaking for the zero-field Sherrington-Kirkpatrick model at zero temperature: the Parisi minimizer is absolutely continuous, has a smooth density, and has support $[0,1)$. At inverse temperature $β>1$, [arxiv.org/abs/2607.11756v3] recently proved that the Parisi measure has support $[0,q_β]$. Here, we show $q_β$ converges to $1$ as $β\to\infty$.
Comments40 pages: 25 main text, 15 appendices/references. Successor to an AI-generated aiXiv preprint. ChatGPT 5.6 is the actual author: it generated the proof arguments and prose. Hong-Bin Chen is formally listed as author only to comply with arXiv policy and accepts full responsibility. A conditional Lean 4 formalization machine-checks Theorems 1.2 and 1.3 from seven identified analytic inputs
