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Specialist consultation delays are a pervasive source of prolonged inpatient stays and disrupted throughput. They remain difficult to anticipate because delay risk emerges across ordering, communication, workload, and completion steps. A predictive model could support earlier recognition of consults likely to exceed expected completion windows. Existing consultation monitoring often depends on retrospective reports, manual tracking, or informal escalation. These approaches miss the opportunity to intervene while the consultation is still unfolding. A real-time model could convert consult workflow events into actionable delay forecasts. This article proposes a sequence learning model that predicts the probability of specialist consultation completion delay at the time of order entry. The model would refine this probability after each subsequent event, including messages, assignment, escalation, note drafting, and completion. The objective is conceptual model development rather than experimental evaluation. The proposed approach uses an LSTM-, GRU-, or Transformer-based architecture to ingest consultation milestones and static context. Inputs include consultation type, patient location, ordering service, specialty workload, communication logs, and escalation history. The output is a dynamically updated delay probability intended for consult workflow management. Conceptually, the model would identify high-risk consults early, such as a complex weekend consultation for a critically ill patient with no timely response from an overloaded service. It would be expected to support targeted escalation, workload redistribution, and proactive communication. No empirical performance claims are made. A sequence learning model could help hospitals move from passive consultation tracking to proactive delay management. By combining temporal workflow events with operational context, the model could support more timely specialist input and reduce avoidable length-of-stay pressure. Future evaluation should focus on safety, fairness, usability, and workflow impact.