But if I were to actually read the posts, that might stir something.
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API优先（API-First）的系统互操作性：L3架构天然具备企业级的系统互操作性。通过标准化API接口，AI生成的结构化内容能够无缝嵌入到券商APP、投顾终端、基金官网以及主流财经媒体的CMS（内容管理系统）中。
There is growing concern that the sycophantic nature of LLM chatbots may be facilitating delusions [hill_they_2025_cap]. If a user with a particular belief queries the chatbot about this belief they are likely to receive a validating response. Conversations can go back and forth for several iterations, lasting hours or even days. Users often report feeling as though they have made a big discovery or learned something new [zestyclementinejuice_chatgpt_2025]. But have they?
In SM64 this covering space structure is used by giving Mario extremely high velocity \(v\) (a tangent vector at Marios position in \(P\)) through a different glitch called “backwards longjump”. The exponential map is then used to move Mario along the geodesic \(\exp_v(t)\) for \(t \in \mathbb{R}\). But due to hardware limitations, only discrete steps \(t_1, \dots, t_k\) for some \(k \in \mathbb{N}\) of this geodesic are actually calculated for collision detection. More on how this is related to the exponential map of Lie groups can be found in my previous post. Throughout this post, I will assume the Lie group of SM64 to have its unit at the position \(p\).