Large language models (LLMs) generate fluent outputs that can be wrong. Unlike humans, who often exhibit cues when providing false information, LLMs produce errors that are difficult to detect because autoregressive decoding provides no mechanism for verifying intermediate reasoning before state progression. We introduce Heaviside Continuity of Rolling Coefficients (HCRC), a verification-first execution framework that reformulates inference as predicate-gated state transitions governed by a Heaviside Gate. HCRC combines model confidence with independent verification signals from a parallel worker architecture, allowing execution to advance only when predefined correctness predicates are satisfied. This prevents invalid intermediate states from propagating, reducing epistemic entropy without modifying the underlying model. We evaluate HCRC on software-engineering and reasoning tasks across thirteen proposers from four providers. On capable proposers, the gate reduces the false-completion rate (FCR) from 4--7% to 0% while remaining latency-competitive and, in some settings, faster than the unwrapped model. On weaker proposers, it converts false completions into honest halts instead of corrupting downstream state. Beyond benchmarking, HCRC has operated for months as the production control plane of an agentic coding environment, authorizing file mutations, verification-driven progress reporting, and memory compaction. These results establish HCRC as a general framework for verification-driven LLM execution, showing that reliable reasoning can be achieved through principled execution control rather than model scale alone.
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.