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定理将协调自由性与单调性联系起来，但该定理局限于关系型转换器和集合包含增长。本文将其推广至任意并发规范描述：规范描述在声明的精化序下将执行历史映射到结果集。我们证明，当且仅当规范描述的结果是单调的时，其才允许无协调实现（完全CALM）。该准则统一了CALM、CRDT、I-汇合与HAT作为特例，支持对适当协调的验证，并衍生出"完全CAP"辅助定理：一个规范描述允许一致性、可用性与分区容错性实现，当且仅当其是分布式单调的。