When two agents of different computational capacities interact with the same environment, they need not compress a common semantic alphabet differently; they can induce different semantic alphabets altogether. We show that the quotient POMDP $Q_{m,T}(M)$ - the unique coarsest abstraction consistent with an agent's capacity - serves as a capacity-derived semantic space for any bounded agent, and that communication between heterogeneous agents exhibits a sharp structural phase transition. Below a critical rate $R_{\text{crit}}$ determined by the quotient mismatch, intent-preserving communication is structurally impossible. In the supported one-way memoryless regime, classical side-information coding then yields exponential decay above the induced benchmark. Classical coding theorems tell you the rate once the source alphabet is fixed; our contribution is to derive that alphabet from bounded interaction itself. Concretely, we prove: (1) a fixed-$\varepsilon$ structural phase-transition theorem whose lower bound is fully general on the common-history quotient comparison; (2) a one-way Wyner-Ziv benchmark identification on quotient alphabets, with exact converse, exact operational equality for memoryless quotient sources, and an ergodic long-run bridge via explicit mixing bounds; (3) an asymptotic one-way converse in the shrinking-distortion regime $\varepsilon = O(1/T)$, proved from the message stream and decoder side information; and (4) alignment traversal bounds enabling compositional communication through intermediate capacity levels. Experiments on eight POMDP environments (including RockSample(4,4)) illustrate the phase transition, a structured-policy benchmark shows the one-way rate can drop by up to $19\times$ relative to the counting bound, and a shrinking-distortion sweep matches the regime of the asymptotic converse.

翻译：当两个不同计算能力的智能体与同一环境交互时，它们不必对一个共同的语义字母表进行差异化压缩，而可能诱导出完全不同的语义字母表。我们证明，商POMDP $Q_{m,T}(M)$（与智能体能力相符的唯一最粗抽象）可作为任何有界智能体的容量推导语义空间，且异构智能体间的通信表现出尖锐的结构相变。低于由商失配决定的关键速率 $R_{\text{crit}}$ 时，保意图通信在结构上不可实现。在支持的单向无记忆场景中，经典边信息编码在诱导基线之上呈现指数衰减。经典编码定理在源字母表固定后告知速率；我们的贡献在于从有界交互本身推导出该字母表。具体地，我们证明：(1) 一个固定$\varepsilon$的结构相变定理，其下界在公共历史商比较上完全通用；(2) 商字母表上的单向Wyner-Ziv基线识别，具备精确逆定理、无记忆商源的精确操作等价性，以及通过显式混合界建立的遍历长期桥梁；(3) 在收缩畸变区域$\varepsilon = O(1/T)$下的渐近单向逆定理，从消息流和解码器边信息证明；以及(4) 对齐遍历界，实现通过中间容量层的组合通信。在八个POMDP环境（包括RockSample(4,4)）上的实验展示了相变现象；一个结构化策略基线表明单向速率相对于计数界可降低高达19倍，而收缩畸变扫描与渐近逆定理区域相匹配。