Geometric Clinical Ethics: Medical Decision-Making as Pathfinding on the Moral Manifold, and the Mathematical Structure of Moral Injury

Clinical medicine is saturated with moral reasoning. Every triage decision, every informed-consent conversation, every resource-allocation judgment, every end-of-life conference is a moral act embedded in a clinical act. Yet the dominant quantitative framework for medical decision-making---the quality-adjusted life year (QALY)---collapses this multi-dimensional moral reality to a single scalar, committing the same dimensional-projection error that classical economics commits with utility maximization. We provide the mathematical framework that clinical ethics has lacked. Drawing on the Geometric Ethics programme , we construct the : a nine-dimensional weighted simplicial complex on which clinical decisions are pathfinding problems. The clinician's decision is modeled as A^* search with evaluation function f(n) = g(n) + h(n), where g(n) is the accumulated clinical cost (evidence-based outcome calculation) and h(n) is the (the clinician's trained ethical intuition: do no harm, respect autonomy, maintain trust). The optimal clinical path---the ---minimizes total cost on the full manifold, not on the scalar projection. The framework yields six results. (1)~The four principles of biomedical ethics (Beauchamp and Childress) are not independent axioms but , and principlism's inability to resolve conflicts between them is a consequence of treating dimensions as incommensurable axioms rather than as components of a metric. (2)~The QALY is a scalar projection that destroys irrecoverable moral information (Scalar Irrecoverability Theorem); QALY-optimal policies can be manifold-suboptimal. (3)~Informed consent is the requirement that the patient's epistemic dimension d_9 and autonomy dimension d_4 be calibrated before the clinical geodesic is computed---a gauge-invariance condition, not a bureaucratic formality. (4)~Moral injury in healthcare workers is mathematically characterized as : the institution requires the clinician to traverse a path whose moral-heuristic cost h(n) exceeds the clinician's boundary tolerance, producing cumulative manifold damage that is distinct from burnout and distinct from PTSD. (5)~Triage is A^* search under catastrophic resource constraints, where the manifold's edge weights shift dynamically as scarcity increases---and the framework predicts when utilitarian triage (maximize lives saved) diverges from manifold-optimal triage (minimize total moral friction). (6)~The clinical Bond Index provides a quantitative measure of the moral cost imposed on patients by institutional policies, enabling empirical detection of structural injustice in healthcare delivery. The framework is immediately testable: it generates falsifiable predictions about clinician decision-making, moral distress scores, and patient-reported ethical experience that differ from predictions of standard bioethics and QALY-based health economics. Author preprint deposited for archival and citation. Draft — pending author review.