二元信任八卦动力学的终止：一个构造性的无极限环定理
Termination of Binary Trust-Gossip Dynamics: A Constructive No-Limit-Cycles Theorem
AI总结：
研究二元信任八卦动力学，通过构造性证明，基于信任链连接的不同代理有序对数量这一降序度量，证明在公平调度下轨迹会在有限步到达吸收态，不存在极限环。
摘要：
在二元信任八卦动力学中，n个代理对其他代理有信任或不信任的有向二元观点，八卦步骤中复制者信任源时可复制观点。证明在任何公平调度下，每个轨迹在有限步到达吸收态，不存在极限环。证明基于信任链连接的不同代理有序对数量这一降序度量。
英文摘要：
In the binary trust-gossip dynamics, $n$ agents each hold a directed binary opinion, trust or distrust, of every other agent, and a gossip step lets one agent copy another agent's opinion of a third whenever the copier trusts the source. We prove that under any fair schedule of such steps, every trajectory reaches an absorbing state in finitely many steps, one in which no gossip step changes any opinion; in particular, there are no limit cycles. The proof is constructive and rests on a single descent measure: the number of ordered pairs of distinct agents linked by a chain of trust. Trust-adding gossip leaves this count unchanged and trust-removing gossip can only lower it, so it never rises, and it is zero only at the all-distrust state. From any non-absorbing state we exhibit a finite run of steps that reaches an absorbing state or strictly lowers the count; since the count is a non-negative integer at most $n(n-1)$, the process halts at an absorbing state.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
