前缀指令与不可压流
Prefix Instructions and Incompressible Flows
OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。
具体内容
稿件研究有限前缀指令可能改变面积并擦除信息的问题，作者给出显式历史处理器与光滑不可压运动，保留信息并在全定义域实现每条指令。首个应用为每台机器与有限输入在平坦单位三维环面上、任意固定正可计算黏度下指定光滑零均值外力；解从静止出发，固定粒子恰在机器停机时进入固定开带，外力在初始加载后周期为一。作者还给出全盒、法向补偿、不变平面与空间时钟等替代实现，并说明初始化、比较类、导数界与连续时间观测。摘要未给证明细节，结论待独立审查。
- 显式历史处理器与光滑不可压运动在全定义域实现每条前缀指令并保留信息
- 对每台机器与输入构造周期外力，固定粒子恰在停机时进入固定开带
- 另给全盒、法向补偿、不变平面与空间时钟等替代实现
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英文原始摘要
Finite prefix instructions may change area and erase information. We give explicit history processors and smooth incompressible motions that retain that information and realize every instruction on its full domain. A first application assigns each machine and finite input a smooth mean-zero force on the flat unit three-torus, at any fixed positive computable viscosity. The solution starts from rest; a fixed particle enters a fixed open strip exactly when the machine halts. The force repeats with period one after an initial loading interval. We then prove alternative realizations using full boxes, normal compensation, invariant planes, and a spatial clock. The constructions specify their initialization, comparison class, derivative bounds, and continuous-time observation. Exact formulas and effective cutoffs provide finite descriptions of the fields and all their derivatives.
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