Incorporating trivial rescaling/relabeling reductions

Develop a reduction or homomorphism framework that captures trivial equivalences induced by rescaling and relabeling of payoffs (such as the equivalence of 3LIN2 and 3LIN2(1,1)) within the algebraic theory of valued PCSPs.

Background

The paper exhibits examples (e.g., 3LIN2 vs. 3LIN2(1,1)) where problems are trivially equivalent but not explained by the current valued minion homomorphism framework. Incorporating these trivial transformations would strengthen the reduction theorem and close gaps between practical reductions and the algebraic theory.

Resolving this would ensure the framework uniformly captures common transformations used in approximation and optimization CSPs.