The widespread adoption of clinical large language models (LLMs) introduces significant risks of automation bias, premature closure, and clinician deskilling. Current interpretability paradigms, including latent space trajectories, Concept Activation Vectors, and Concept Bottleneck Models, suffer from topological stagnation, metric distortion, and epistemic occlusion, frequently masking intermediate diagnostic uncertainty behind falsely confident outputs. To address these structural vulnerabilities, this paper introduces a novel closed-loop, multi-agent framework designed to quantify and visualize dynamic epistemic uncertainty in clinical LLM reasoning. By coupling predictive Shannon entropy with non-linear Isometric Feature Mapping (ISOMAP), the architecture projects high-dimensional inference state vectors onto a calibrated two-dimensional latent space, thereby assigning a quantifiable thermodynamic energy state to the reasoning path to track diagnostic velocity, cognitive momentum, and trajectory efficiency across sequential diagnostic rounds. Pilot validation across representative emergency medicine scenarios demonstrated distinct topological and information-theoretic behaviors: unconfounded cases (cerebellar infarction) exhibited smooth geodesic progression toward the ground truth alongside monotonic Shannon entropy decay from 2.15 to 1.74; noisy environments with ambiguous findings (spontaneous pneumothorax) suffered from trajectory wandering, local minimum traps, and high sustained entropy (~2.41) due to insufficient repulsive weighting for negative evidence; and triage-conflicted cases (acute cholangitis) achieved precise geometric proximity to the true node but experienced top-1 rank stagnation because the model conflated acute severity triage (sepsis) with anatomical etiology. By rendering machine hesitation and cognitive divergence visually auditable before final diagnostic crystallization, this geometric-information framework enables dynamic trust calibration and human-AI co-regulation at the point of care while establishing a clear mathematical foundation for future architectural interventions, such as dual-channel safety decoupling and non-linear repulsive weighting. Moving forward, validating these architectural enhancements across large-scale electronic health record databases and prospective clinical trials will be essential to realize its full clinical utility, establishing a foundational blueprint for safe, transparent, and cognitively synergistic AI integration in future medical practice. By rendering the LLM's reasoning process visually auditable, this framework lays the groundwork for capturing and externalizing the clinician's own cognitive patterns within the AI, forming a coupled system. This enables the explicit visualization of cognitive gaps between physician hypotheses and AI inferences, transforming the interaction from simple answer-checking into a dynamic learning process for both human and machine that prevents diagnostic oversight. Ultimately, because the responsibility for final clinical decision-making remains with the human practitioner, this framework serves as a vital decision-support mechanism. Moving forward, validating these architectural enhancements across large-scale electronic health record databases and prospective clinical trials will be essential to realize its full clinical utility, establishing a foundational blueprint for safe, transparent, and cognitively synergistic AI integration in future medical practice.