Problem. The explanation of nuclear properties from the strong force upwards has been elusive. Approach. Design methods were used to develop conceptual mechanics for the bonding arrangements between nucleons, based on the covert structures for the proton and neutron as defined by the Cordus theory, a type of nonlocal hidden-variable design with discrete fields. Findings. Nuclear bonding arises from the synchronous interaction between the discrete fields of the proton and neutron. This results in not one but multiple types of bond, cis-and transphasic, and assembly of chains and bridges of nucleons into a nuclear polymer. The synchronous interaction constrains the relative orientation of nucleons, and hence the nuclear polymer takes only certain spatial layouts. The stability of nuclides is entirely predicted by morphology of the nuclear polymer and the cis-/transphasic nature of the bonds. The theory successfully explains the qualitative stability characteristics of all hydrogen and helium nuclides. Originality. Novel contributions include the concept of a nuclear polymer and its mechanics; an explanation of the stability, instability, or nonexistence of nuclides starting from the strong/synchronous force; explanation of the role of the neutron. The theory opens a new field of mechanics by which nucleon interactions may be understood.