PFUSRC-043: The Principle of Least Action Is Not a First Principle — A Proof from PFUSRC Biconic Topology

Based on the ontological framework of PFUSRC biconic topology, this paper proves that the principle of least action and its mathematical expression, the Lagrangian equation, are not fundamental first principles governing cosmic evolution. The Lagrangian equation is demonstrated to be a degenerate special case derived from PFUSRC dual-field dynamics under three ideal limiting conditions: waist-ring steady state with zero action variation, absence of external perturbations, and constant single-anchor state of the Ψ-field. The unique optimal path solved by the classical calculus of variations is merely a mathematical product under such ideal constraints, which cannot reflect real physical processes. In nature, physical evolution is dominated by Ψ-Ξ dual-field anchoring and gap-field transitions, where continuous trajectories and unique extremal values do not exist. This study achieves the theoretical falsification and replacement of the principle of least action. It clarifies the actual application scope of the classical calculus of variations: it is an effective mathematical tool only under specific ideal assumptions, rather than an ontological law of the universe.