An axiomatic framework for the temporal structure of quantum pure states is formulated. In addition to time-reversal symmetry, two ontological postulates are introduced: binary reality and coherent composition. A physically complete pure state is required to contain two distinct time-reversal-related branches with a definite relative phase. We prove that, for a time-reversal-covariant Hamiltonian, the reversed branch obtained by applying the antiunitary time-reversal operator to the time-reflected forward solution satisfies the same Schrödinger equation. Linearity and coherent composition then imply a coherent superposition of the two partners. The theorem does not require different energy eigenvalues: the partners may lie in the same degenerate eigenspace. The result is therefore a conditional theorem of the enlarged axiomatic framework rather than a derivation of quantum superposition from standard time-reversal symmetry alone.