Rejecting inputs outside the defined in-distribution (IND) service scope is critical for large language model (LLM) services, where unsupported requests should be filtered before full generation. Existing out-of-distribution (OOD) detectors often rely on final outputs or final-layer representations, leaving unclear where service-boundary signals are most clearly encoded inside the model; they also lack a theoretical guarantee for held-out inputs. In this paper, we introduce SCOPE (Sequential Conformal OOD Probing and Evaluation), a framework that selects a readable hidden layer, constructs a conformal gate with IND calibration, and uses a supermartingale e-process to certify persistent service-boundary evidence. Experiments across multiple LLM backbones and six carefully designed boundary conditions show that SCOPE improves gate-level rejection over standard final-layer detectors, while revealing how different OOD boundaries take different geometric forms in hidden space.
In black-box large language model (LLM) services, response reliability is often only partially observable at decision time, while stronger inference pathways incur substantial computational cost, inducing a budgeted sequential decision problem: for each request, the system should decide whether the default low-cost response is sufficiently reliable or whether additional computation should be allocated to improve response quality. In this paper, we propose \textbf{Ver}ifiable \textbf{O}bservations for Risk-aware \textbf{I}nference \textbf{C}ontrol (\textsc{Veroic}), a framework for adaptive inference control in black-box LLM settings, which formulates request-time control as a \textit{partially observable Markov decision process} to capture partial observability and sequential budget coupling. It constructs a lightweight verifiable observation channel from the input-output pair by aggregating heterogeneous quality signals into a belief state over latent response reliability, which is then used by a budget-aware policy to decide whether to return the default output or trigger a higher-cost inference pathway. Experiments on diverse tasks show that \textsc{Veroic} achieves improved quality-cost trade-offs, stronger risk estimation and calibration, and more robust long-horizon inference control than competitive baselines.