Executable Semantic Survival in Language-Model Relays

Repeated language-model communication can substantially change a message while preserving what a receiver does with it. Surface similarity therefore does not determine operational meaning, and one-step retention may not predict long-horizon semantic survival. We formalize this distinction by defining two messages as equivalent when a frozen receiver selects the same action in the same task context, inducing a context-conditioned executable semantic quotient. We characterize when this quotient evolves as a closed Markov process via strong lumpability and bound the error of approximate closure over finite horizons. To study long-horizon preservation, we stop a trajectory at its first action change and represent the surviving dynamics with a killed operator. Its powers recover the full first-passage survival law, revealing how equal one-step retention can hide different futures because surviving mass may occupy different within-fiber states. We further analyze observable repair using only public messages and receiver outputs, and use two frozen receivers to form survival bounds under evaluator ambiguity. Controlled constructions verify the theory. Empirically, in open-model relays up to 35B parameters, natural messages with identical current actions can still diverge under matched future rewrites, while killed-operator predictions outperform repeated one-step retention, including for held-out receivers. Together, these results show that semantic stability is a trajectory property: a message can be executable now yet be only metastably executable under repeated transmission.