This paper demonstrates the practical application of MCR-10 (Mathematical Cognitive Reconstruction) through a detailed case study of a historically documented decision sequence. Using evidence-anchored constraints, bounded hypothesis classes, and explicit validation, we reconstruct the minimal feasible cognitive set underlying a specific decision event. The case study illustrates how MCR-10 avoids speculative psychology, handles irreducible non-uniqueness, and produces a structured,reproducible cognitive explanation. The analysis also integrates the 12 Canonical AI Findings mapped to the 8 AI Layers,showing how modern AI systems differ fundamentally from human cognition and why constraint-based reconstruction isnecessary for historical modeling.