Finite Adjoint-Transform Orbits for Funcoids and Reloids

For a monotone map between complete lattices, let its two adjoint transforms be the supremum of sublevel sets and the infimum of superlevel sets. Porton's diagram problem asks for the missing transform of the outward reloid map and whether its iterated transforms form a finite set. Working in ZFC, we identify the missing map as the join of the induced funcoid with the product of the two Frechet filters. We give a closed transition table containing at most twenty typed maps, thereby proving finiteness for arbitrary source and destination sets. If either set is finite, at most two maps occur. The proof uses Todd Trimble's representation of funcoids by closed subsets of a product of Stone spaces, together with two density statements about nonsingleton fibers of the canonical Stone map. We also give a counterexample to an extra arrow in the published diagram. Twenty is an upper bound, not a claim that all its labels are distinct or that the bound is optimal. This is an unrefereed, AI-assisted preprint.