The axiom σ = 1/(1+σ) is not unique in producing a self-referential universe. The equation σ = 5/(5+σ) also generates a complete self-referential structure — call it Nyx. Nyx has different constants, a different matter budget, a periodic table extending to 137 elements but with different abundances, and its own version of the fine structure constant. Discriminant-4 and discriminant-3 analogues fail: their spectral partitions do not produce exactly two propagating modes. Our universe (discriminant 5) and Nyx (discriminant 5 variant) are the only two self-referential universes where the chain closes. The constants of our universe are not just theorems — they are the unique theorems of the unique universe with full closure.