发表机构
University of Cape Town（开普敦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对层级因果系统中反身性的实现问题，提出依赖状态的时间变化方法，明确跨层约束与事件协调，揭示反身性为因果回路的内生闭合。
AI 中文摘要
我们研究层级因果系统中的反身性，其中高层状态约束仍可容许的低层动力学[Wilcox和Gebbie（2014），Gebbie（2026）]。我们探讨当局部活动是事件驱动且因果主张在日历时间中提出时，这种依赖状态的自上而下约束如何实现。若由参与者条件约束同时支配可容许的事件转移及其时间，事件过程会通过依赖状态的时间变化被带入日历时间。若可容许约束或兼容时间法则不唯一，即使局部事件动力学允许马尔可夫表示，诱导的日历时间因果法则也不必唯一。层级因果性明确保留跨层约束和事件协调，而日历时间法则必须由这些要素构建。在该层级表示中，反身性是通过依赖状态的自上而下约束及事件到日历时间映射形成的因果回路的内生闭合。
英文摘要
Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated within such a discrete hierarchical causal system; but one in which a higher-level actor state restricts the lower-level transition kernels that remain admissible. Then event dynamics can be separated from calendar embeddings: a set-valued actor-conditioned correspondence can be used to define the admissible family of event kernels, while joint state and waiting-time laws can be used to determine compatible timing to then natural demonstrate reflexivity. A selected event-state law need not determine a unique calendar embedding. Locally, uniqueness of the joint event or timing specification requires uniqueness of both the admissible event kernel and its compatible timing law. Reflexivity is thus the endogenous closure of a hierarchical constraint loop, while timing and projection can generate calendar-time memory or causal ambiguity even for Markov event dynamics.
Comments9 pages, 3 figures, 3 appendices with expanded exposition an figure to improve the idea presentation based on community feedback
