An Extended Action for the Three-Point Discrete Burgers Equation

We construct a local extended action for the full nonlinear three-point discrete Burgers equation. Independent adjoint variables recover every original lattice equation, and a zero-adjoint lift proves exact equality between the original solution set and the projection of the stationary set. A separate action using only the original field is proved equivalent on arbitrary finite causal rectangles with fixed inflow and freely varied outflow. An explicit counterexample shows why this finite-domain proof does not extend to unrestricted whole-lattice least squares. The established formal-Lagrangian construction is distinguished from the unresolved multiform question. The deposit includes the manuscript, reproducible Lean sources, and a precise statement of the verified scope.