We study horizon-uniform local branches of finite-horizon discrete-time Pontryagin boundary value systems after smooth control elimination. The central input is a two-point endpoint inverse for the linearization. We verify this inverse from scaled stable--unstable boundary transversality, prove the associated endpoint-corrected Green estimate, and combine it with weighted contractions to obtain existence, uniqueness, Lipschitz dependence, and first-order expansions with constants independent of the horizon. The framework covers smooth nonlinear endpoint maps, including the original Pontryagin rows that fix the initial state and couple the terminal costate to the terminal state. Symplectic and Riccati criteria verify the inverse hypothesis at the level of the matrix data; in particular, every stabilizable linear-quadratic system with invertible dynamics and definite weights is covered, including noncommuting coupled data. A numerical section illustrates the certificates and the horizon-uniform first-order expansion.

翻译：[translated abstract in Chinese] 在光滑控制消去后，我们研究有限时域离散时间庞特里亚金边值系统的水平一致局部分支。核心输入是线性化后的两点端点逆映射。我们通过缩放稳定-不稳定边界横截性验证了该逆映射，证明了相关联的端点校正格林估计，并结合加权压缩迭代获得了存在性、唯一性、Lipschitz依赖性以及常数不依赖于时域的一阶展开。该框架涵盖光滑非线性端点映射，包括固定初始状态并将终端协态耦合至终端状态的原始庞特里亚金行结构。辛性与Riccati准则在矩阵数据层面验证了逆假设；特别地，每个具有可逆动力学和确定权重的可镇定线性二次系统均被覆盖，包括非交换耦合数据的情形。数值实验部分展示了验证过程及水平一致一阶展开。