Debates about artificial intelligence (AI) safety often reach for P(doom), a shorthand in AI-safety discussions for the probability of catastrophic AI risk. Healthcare needs a nearer and more testable companion: P(harm), a proposed surveillance framework for cumulative clinical risk. We define accumulative risk as harm that arises from repeated small shifts in diagnosis, triage, clinician behavior, training, or workflow rather than a single catastrophic failure. We operationalize P(harm) as a family of workflow-specific, severity-weighted conditional estimates: in a declared workflow and model version, it is the estimated probability that an independently reviewed AI-exposed encounter has an adverse outcome of at least a prespecified severity within a prespecified time horizon, after stratifying or adjusting for acuity, case mix, and local workflow covariates. In pilot use, the estimator should be prespecified, for example, a risk-adjusted empirical incidence with confidence or credible intervals or a hierarchical logistic/Bayesian model; P(harm) is not a causal-attributable fraction unless paired with a valid comparison design. The framework is organized around four local pathways—AI–clinician discordance in complex patients, automation bias, skill erosion and never-skilling, and consumer AI triage failure—plus a fifth, less mature pathway for correlated vendor or foundation-model failures across institutions. The motivating evidence is early and heterogeneous, often retrospective or vignette-based, so each pathway is framed as a surveillance hypothesis rather than proof of generalized harm. The purpose is not to slow beneficial AI, which may reduce errors and administrative burden, but to make clinical drift visible early enough for health systems to adjudicate, recalibrate, roll back, or retrain before repeated small failures accumulate.