Silence as an Optimal Action: A Decision-Theoretic Foundation for the In-Cabin AI Companion

Voice assistants are engineered on the implicit premise that speaking is free and silence is failure. Deployed inside a moving vehicle, this premise inverts: every utterance competes for a driver's finite attention in a safety-critical environment, and a wrong or ill-timed utterance carries measurable cost. We present a decision-theoretic foundation for in-cabin conversational AI in which silence is a first-class action, selected, like any other speech act, by minimizing expected loss under uncertainty. The framework is not proposed but deployed: it is extracted from CN4C, a production in-cabin companion running on a consumer smartphone coupled to a vehicle's diagnostic bus, and every constant and measurement in this paper cites its implementation or its field data. We make four contributions. (1) An expected-loss turn policy that decides act / ask / remain silent from a cost ratio elicited from the deployment context, with its decision boundary derived rather than tuned (p* = 0.25 at a 1:3 interruption-to-omission cost ratio); evaluated on 269 blind-labeled field turns it achieves held-out F1 = 0.891 against 0.706 for the production binary gate, raising recall on genuine driver requests from 0.370 to 0.901 at an essentially unchanged interruption rate. (2) Certified speech under location uncertainty: a fusion of classification-with-reject-option and robustness certification in which a location-conditioned utterance is emitted only when the entire GPS uncertainty disc lies within a single semantic zone; we formalize the deployed 8-point boundary probe, prove its soundness margin (cos(π/8) on convex zones), and give the exact certificate that closes its gap. (3) A refractory model of proactivity: machine-initiated speech as a timed process governed by priority preemption and per-channel refractory periods, with all parameters instantiated in production. (4) A conjunctive trust accumulator that gates the agent's expressive envelope (humor, vulnerability, proactivity) on the minimum of three interaction axes (elapsed relationship time, shared episodes, and kilometres travelled together), so that intimacy is earned monotonically and cannot be configured. We show that each ingredient is established mathematics proven in other domains (optical character recognition, clinical decision support, desktop attention management, adversarial robustness) that has, to our knowledge, never been composed into, or applied to, the in-car interaction problem. We situate the framework as the embodied continuation of the author's System 0 / HCNC program, and close with the pilot deployment's measurements and limitations.