The CALM theorem connects coordination-freedom to monotonicity, but is tied to relational transducers and set-inclusion growth. We generalize it to arbitrary concurrent specifications. A specification maps execution histories to outcome sets under a declared refinement order; we prove it admits coordination-free implementation if and only if its outcomes are monotone (\emph{Complete CALM}). The criterion subsumes CALM, CRDTs, I-confluence, and HATs as instances, enables verification of proper coordination, and yields a \emph{Complete CAP} companion: a specification admits a consistent, available, partition-tolerant implementation if and only if it is distributed-monotone.

翻译：CALM定理将协调自由与单调性联系起来，但该定理局限于关系型转换器与集合包含增长。我们将其推广至任意并发规范。规范将执行历史映射至声明细化序下的结果集；我们证明，当且仅当规范的结果具有单调性时，该规范允许无协调实现（完全的CALM）。该准则将CALM、CRDT、I-汇合与HAT作为特例进行归约，能够验证恰当的协调性，并衍生出完全的CAP伴侣：一个规范当且仅当它是分布式单调时，才允许实现一致性、可用性与分区容错性。