Large language models, LLMs, are increasingly deployed in multiturn settings where earlier responses shape later ones, making reliability dependent on whether a conversation remains consistent over time. When this consistency degrades undetected, downstream decisions lose their grounding in the exchange that produced them. Yet current evaluation methods assess isolated outputs rather than the interaction producing them. Here we show that conversational structural consistency can be monitored directly from token frequency statistics, without embeddings, auxiliary evaluators or access to model internals. We formalize this signal as Bipredictability, P, which measures shared predictability across the context, response, next prompt loop relative to the turn total uncertainty, and implement it in a lightweight auxiliary architecture, the Information Digital Twin, IDT. Across 4,574 conversational turns spanning 34 conditions, one student model and three frontier teacher models, P established a stable runtime baseline, aligned with structural consistency in 85 percent of conditions but with semantic quality in only 44 percent, and the IDT detected all tested contradictions, topic shifts and non-sequiturs with 100 percent sensitivity. These results show that reliability in extended LLM interaction cannot be reduced to response quality alone, and that structural monitoring from the observable token stream can complement semantic evaluation in deployment.