= Solution
At coincidence $\phi_1=\phi_2$, the <triplet state> spatial factor vanishes, while the lowest <singlet state> has finite, uniform pair <probability>. Consequently a weak short-range repulsion raises the <singlet state> <energy> more strongly: \b[antisymmetry suppresses close encounters in the <triplet state>]. In the contact-interaction limit the <triplet state> contribution is exactly zero, whereas the <singlet state> shift is positive. A finite-range interaction gives a nonzero but suppressed <triplet state> shift. This explains a relative <energy> increase; it does not by itself establish a crossing or justify using unchanged noninteracting <wavefunctions> for arbitrarily strong repulsion.
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