Coherent-pair conjecture for non-trivial maps of coherent cohomology

Let $(\pi,\pi')$ be a coherent pair linked by the chain of diagrams constructed in the paper to an elementary pair $(\sigma,\sigma')$. Coherent-pair cohomology conjecture. This chain similarly gives rise to a non-trivial map of coherent cohomology. The conjecture seeks to extend the non-trivial cohomology maps known for elementary pairs to arbitrary coherent pairs through the translation diagrams.