Co-NP-completeness of finite-support Gardens of Eden and rectangular orphans

For the Game of Life, consider finite-support Gardens of Eden and rectangular orphans, with the encodings specified in the paper and polynomial-time many-one reductions. Co-NP-completeness conjecture. Finite-support Gardens of Eden and rectangular orphans are co-NP-complete. The paper establishes a polynomial-time reduction from finite-support Gardens of Eden to orphans but does not provide a converse reduction, so the claimed completeness remains open.