The Vessel Without a Bottom: The Graal, Leonardo’s Geometric Theology, and the Equilibrium Ledger

This expanded monograph develops a structural analysis of sacred geometry, architectural survival, and the Equilibrium Ledger. Through a comparative examination of the Grail romances, Leonardo da Vinci’s Last Supper, the Pantheon, Hagia Sophia, Brunelleschi’s Dome, the Vitruvian Man, and the Salvator Mundi, the study proposes that these works repeatedly confront the same structural problem: how systems under pressure register imbalance, absorb rupture, redistribute force, and survive correction without collapse. The Grail evolves from sacred object to structural function, while Leonardo relocates the sacred centre from vessel to geometry. Architecture becomes a laboratory of equilibrium, demonstrating how forms endure theological, political, and historical transformation. The Equilibrium Ledger is presented as the theoretical vocabulary that formalises these recurring patterns across myth, art, architecture, and symbolic systems.