The Computable Boundary of the Firm: Information Conditions for Viability and the Transactional Architecture of the Digital Twin

In the practice of digital twins of organizations (DTOs), the boundary of the enterpriseis often not instantiated as an independent object of the control model. This paper developsa stochastic model of the firm as a controlled Markov process in which actor membership,interface permeability, and operational dynamics are integrated into a single object of control,while viability is defined as the retention of an essential variable within the homeostatic set K.A necessary condition for viability in a nonstationary, overloading environment is proved:boundary representation—namely, observability of the membership of causally significant actorsand tunability of permeability—is necessary to prevent asymptotic collapse (Theorem 1). Aconditional sufficiency result is also formulated: if the representation makes it possible toconstruct a policy with compensated overload and Lyapunov drift toward an optimum, then thesystem preserves practical (recurrent) viability (Theorem 2). The bridge “residual entropy ⇒positive risk” is derived through an explicit anti-concentration lemma (Lemma 2), rather thanpostulated. Distributed and centralized representations are equivalent in policy expressivenessunder the idealization of synchronous communication (Theorem 3); when one moves to anasynchronous model with losses, they diverge: a communication lower bound Ω(|N (a)|) appliesto distributed labeling (Lemma 3), whereas a consistency–availability dichotomy applies to thecentralized case (Lemma 4), yielding regime-dependent dominance of centralization with respectto the communication component of context-grounding costs (Theorem 4). The engineeringimplication is the pattern of an Executable Boundary Actor, Actor∂S