We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic objects required for such settings and to establish their first theorem-supporting consequences. The paper develops a regime-varying framework centered on admissible transport, protected-core preservation, and evaluator-aware learning evolution. It records the immediate closure consequences of admissibility, develops a structural obstruction argument for faithful fixed-ontology reduction in genuinely multi-regime settings, and introduces a protected-stability template together with explicit numerical and symbolic witnesses on controlled subclasses, including convex and deductive settings. It also establishes theorem-layer results on evaluator factorization, morphisms, composition, and partial kernel-level alignment across semantically commensurable layers. A worked two-regime example makes the admissibility certificate, protected evaluative core, and regime-variation cost explicit on a controlled subclass. The symbolic component is deliberately restricted in scope: the paper establishes a first kernel-level compatibility result together with a controlled monotonic deductive witness. The manuscript should therefore be read as introducing a structured learning-theoretic framework for regime-varying learning together with its first theorem-supporting layer, not as a complete quantitative theory of all learning systems.

翻译：本文研究环境变化下的学习问题，其中学习器、其记忆状态及评估条件可能随时间演化。本文是一项基础性结构性贡献：旨在定义此类场景所需的核心理念对象，并建立其首个定理支撑性结论。文章构建了以可容许传输、受保护核心保留及评估器感知学习演化为核心的变环境框架。记录了可容许性的直接闭包推论，发展了针对真正多环境设置中忠实固定本体约简的结构性障碍论证，并引入受保护稳定性模板，同时在受控子类（包括凸性和演绎性设置）上给出了明确的数值与符号实证。进一步确立了关于评估器分解、态射、组合以及跨语义可通约层的部分核级对齐的定理层结果。通过一个双环境实例，在受控子类上显式给出了可容许性证书、受保护评估核心及环境变化代价。符号组件在范围上受到刻意限制：本文建立了首个核级兼容性结果及受控单调演绎实证。因此，本文应被解读为引入变环境学习的结构化理论框架及其首个定理支撑层，而非所有学习系统的完整定量理论。