Beyond Maximum Likelihood: Deterministic Topological Engineering and H-Infinity Containment in Next-Generation Clinical Diagnostics

Abstract

Modern medical education, codified by the USMLE evaluation paradigm, traditionally trains physicians to execute clinical decisions using Maximum Likelihood Estimation (MLE). We formally establish that this probabilistic heuristic, mathematically isomorphic to an H-2 expected-value optimization, encounters strict topological boundaries when applied to the highly asymmetric thermodynamic penalties associated with orthogonal "fat-tail" differential diagnoses. To safely navigate these rare but critical boundary intersections, this paper introduces the Chrysene Formalism, which maps the undifferentiated patient into a discrete tensor space. The clinical differential is cooperatively redefined as an Orthogonal Pathology Basis, representing a superposition of discrete topological manifolds rather than a continuous Bayesian probability distribution. We formulate a deterministic Clinical Decision Support System (CDSS) governed by an H-infinity min-max objective function. This robust control algorithm strictly minimizes the supremum of thermodynamic strain across all superposed diagnostic manifolds and multivariable organ boundaries simultaneously, safely bounding the patient from topological scission. Through in silico simulations of high-risk USMLE-style clinical vignettes (e.g., Acute Coronary Syndrome vs. Thoracic Aortic Dissection) and a macroscopic Graph Laplacian network model of patients, we computationally validate the safety and superiority of the H-infinity containment protocol. The simulations confirm that prioritizing diagnostic resolvent operators and mathematically derived empiric bridging interventions structurally mitigates the boundary vulnerabilities inherent to the H-2 standard-of-care. Ultimately, we provide a rigorous mathematical framework to gently augment medical evaluation, transitioning clinical epistemology from stochastic approximation to deterministic topological engineering.