Large language models (LLMs) can produce fluent outputs that may be incorrect. Unlike humans, LLMs lack cues indicating errors, as autoregressive decoding does not verify intermediate reasoning. 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 progress only when predefined correctness predicates are satisfied. This prevents invalid intermediate states from propagating, thereby reducing epistemic entropy without altering the underlying model. We evaluated HCRC on software-engineering and reasoning tasks across thirteen proposers from four providers. On capable proposers, HCRC reduced the false-completion rate (FCR) from 4-7% to 0%, remaining latency-competitive and sometimes faster than the unwrapped model. For 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, demonstrating that reliable reasoning can be achieved through principled execution control rather than model scale alone.