A uniform ladder of mass \(M\) and length \(L\) leans at an angle \(\theta\) against a frictionless vertical wall, with its base resting on a rough horizontal floor. A painter of mass \(m\) slowly climbs up the ladder from the base toward the top while the ladder remains stationary. Which of the following claims correctly describes what happens to the magnitude of the static friction force exerted by the floor on the ladder as the painter climbs higher, and provides the correct physical justification?