刺激系统的公理式共享介质协调
Axiomatic shared-medium coordination for stigmergic systems
AI总结：
本文针对刺激系统构建了介质无关的比较框架，通过商纤维的响应适配性分析解决元数据细化问题，在动态层面验证了匹配写操作等性质，并在两类介质中完成实例化。
AI中文摘要：
刺激（stigmergic）协调有许多与介质相关的形式化表述。本文构建了一个与介质无关的比较层，其比较对象为抽象的响应启用签名。对于元数据细化，我们证明：当每个商纤维（fiber）都与响应对齐时，粗商（coarse quotient）恰好具备响应适配性；若不满足该条件，则存在一个规范的最粗响应适配修复，且所有响应适配修复必须至少保留对应纤维方向上的响应类数量。在动态层面，与商兼容的匹配写操作（matched writes）可保留单步行为，新鲜度条件下的操作会产生单步不可提升性障碍，而匹配的单步结果可提升至有限串行轨迹。这些结果在元组空间介质和带时间戳的虚拟刺激数据空间中得到实例化，最终形成一个具有明确正负定理循环的介质无关比较框架；更丰富的路径式与并发语义不在本文研究范围内。
英文摘要：
Stigmergic coordination has many medium-specific formalizations. This paper formulates a medium-agnostic comparison layer whose comparison object is the abstract enabled-response signature. For metadata refinements, we prove that a coarse quotient is response-adequate exactly when each quotient fiber is response-aligned. When that fails, there is a canonical coarsest response-adequate repair, and every response-adequate repair must retain at least the corresponding fiberwise number of response classes. On the dynamic side, quotient-compatible matched writes preserve one-step behavior, freshness-conditional actions yield a one-step non-liftability obstruction, and the matched one-step result lifts to finite serial traces. These results are instantiated for a tuple-space medium and a timestamped virtual-stigmergic dataspace. The result is a medium-agnostic comparison framework with one explicit positive/negative theorem cycle; richer pathwise and concurrent semantics remain outside scope.
