标题： 记忆作为结构轨迹：持久同调与上下文层论 显示英文标题

标题： Memory as Structured Trajectories: Persistent Homology and Contextual Sheaves

摘要： 我们提出了一种基于尖峰时间动力学结构、持续同调性和上下文-内容不确定性原理（CCUP）的记忆和推理的拓扑框架。 从观察到多时程神经组（PNGs）编码由轴突延迟和突触可塑性塑造的可重复、时间锁定的尖峰序列这一现象出发，我们构建了时空复形，其时间一致的转换定义了鲁棒激活循环的链复形。 这些激活环被抽象为单元偏序集，从而实现了具有重叠和组合记忆痕迹的紧凑且因果有序的神经活动表示。 我们引入了delta同调类比，将记忆形式化为一组稀疏、拓扑不可约的吸引子。 一个类似狄拉克delta的记忆痕迹被识别为认知状态潜在流形上的非平凡同调生成元。 这些痕迹沿着可重复的拓扑循环 sharply 局部化，并且仅在推理轨迹完成一个完整循环时被激活。 它们编码了不能仅从局部特征合成的最小路径依赖记忆单元。 我们将这些delta同调生成元解释为低熵内容变量，而高熵上下文变量则以过滤、上同调类或同一潜在空间上的层的形式进行对偶表示。 推理被重新表述为内容与上下文之间的动态对齐，连贯的记忆检索对应于选择并维持拓扑生成元的全局截面的存在。 记忆不再是静态吸引子或分布式代码，而是一个完成循环、具有结构意识的推理过程。 显示英文摘要

摘要： We propose a topological framework for memory and inference grounded in the structure of spike-timing dynamics, persistent homology, and the Context-Content Uncertainty Principle (CCUP). Starting from the observation that polychronous neural groups (PNGs) encode reproducible, time-locked spike sequences shaped by axonal delays and synaptic plasticity, we construct spatiotemporal complexes whose temporally consistent transitions define chain complexes over which robust activation cycles emerge. These activation loops are abstracted into cell posets, enabling a compact and causally ordered representation of neural activity with overlapping and compositional memory traces. We introduce the delta-homology analogy, which formalizes memory as a set of sparse, topologically irreducible attractors. A Dirac delta-like memory trace is identified with a nontrivial homology generator on a latent manifold of cognitive states. Such traces are sharply localized along reproducible topological cycles and are only activated when inference trajectories complete a full cycle. They encode minimal, path-dependent memory units that cannot be synthesized from local features alone. We interpret these delta-homology generators as the low-entropy content variable, while the high-entropy context variable is represented dually as a filtration, cohomology class, or sheaf over the same latent space. Inference is recast as a dynamic alignment between content and context and coherent memory retrieval corresponds to the existence of a global section that selects and sustains a topological generator. Memory is no longer a static attractor or distributed code, but a cycle-completing, structure-aware inference process.