Noether's theorem guarantees that every differentiable symmetry of the action of a physical system has a corresponding conservation law in both Lagrangian and Hamiltonian mechanics, making this a foundational standard in theoretical physics.
The claim states a fundamental mathematical and physical principle taught in introductory and advanced analytical mechanics. The retrieved papers do not specifically test or challenge this exact formulation in a hypothesis-driven way, but rather rely on or extend Noether's theorem in various contexts (such as multicontact field theories [8]). Because this relationship between symmetries and conserved quantities is a definitional and foundational pillar of classical field theory and analytical mechanics, no specific citation is needed.