It has long been expected in physics that there should be causality from the strong nuclear force to nuclear structures, but the mechanisms have been unknown. The present work addresses this problem, by developing a theory based on a non-local hidden-variable (NLHV) design, that explains the nuclides from the synchronous interaction (strong force) upwards. The basis of the Cordus nuclear theory is that the nucleus consists of a nuclear polymer bonded by the synchronous interaction (strong force). Three-nucleon physics are accommodated, in the form of bridge neutrons across the nuclear polymer. The requirements for nuclide stability are identified as the need to have a nuclear polymer that consists entirely of cis-phasic synchronous bonds, and also a spatially viable layout. Only certain identified layouts are viable. The Cordus nuclear theory successfully explains, for all nuclides from Hydrogen to Neon, why any nuclide is stable, unstable, non-viable or non-existent. It explains why some elements have multiple nuclides, and others only one. The theory also explains the deviations from the p=n line, why 1H0 and 2He1 are stable with low neutron counts, why 4Be4 and 9F9 are unstable, and why heavier elements require more neutrons than protons for stability. It explains relative stability (lateral trends with one nuclide series), including the anomalous progressions (i.e. those situations where one nuclide is unexpectedly much more or less stable than its neighbouring nuclides). The theory also explains why the limits of stability are where they are. It explains the patterns of stability in the table of nuclides, such as the runs of stable isotopes and stable isotones. Thus the nuclide landscape may be explained by morphological considerations based on a NLHV design.