Artificial Intelligence Triage for Snakebite Envenoming Under Variable Antivenom Stock Records: A Constraint-Aware Evaluation of Healthcare Referral Timing in District Hospitals

District hospitals in snakebite-endemic regions frequently decide whether to refer a patient to a tertiary centre before antivenom availability is confirmed, and the resulting referral timing error is a function of both clinical uncertainty and stock-record uncertainty. the present analysis formalises that decision as a constrained triage problem in which the triage policy observes a noisy antivenom stock signal and must choose between holding the patient and referring immediately. A constraint-aware triage model is developed that separates clinical severity estimation from stock-record reliability, and a formal analysis establishes conditions under which the optimal referral threshold shifts as a function of record reliability. The model is evaluated through a replication-based design characterisation of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells. The analysis indicates that 54 clusters are required to detect a 5 percentage-point effect at 80% power, and that the minimum detectable effect at 80% power declines as cluster count increases from 8 to 32. The contribution is a formal statement of how stock-record unreliability propagates into referral-timing error, and a demonstration that triage thresholds calibrated on clinical severity alone are systematically miscalibrated when stock records are noisy.