= Solution
The weak <charged current> couples an <Up quark>[up-type quark] to the rotated down field $d'_{iL}=\sum_jV_{ij}d_{jL}$. A <neutral current> is <Flavor eigenstate>[flavour] universal within equal-charge <quarks>. Rotating it into the <mass> basis therefore gives
$$
\sum_i\bar d'_{iL}\gamma^\mu d'_{iL}
=\sum_{j,k}\bar d_{jL}\gamma^\mu(V^\dagger V)_{jk}d_{kL}
=\sum_j\bar d_{jL}\gamma^\mu d_{jL}.
$$
The off-diagonal terms vanish by <CKM matrix>[CKM unitarity], so no tree-level <Flavor-changing neutral current>[flavour-changing neutral current] is generated. In the two-generation description, the orthogonal strange-charm partner completes the <rotation> whose single down-strange combination alone would have produced an off-diagonal neutral coupling. The complete multiplet supplies the cancellation.
At <Loop diagram>[loop] level, a flavour-changing <Probability amplitude>[amplitude] has the structure
$$
\mathcal A_{a\to b}\propto\sum_iV_{ai}V_{bi}^*F(m_i^2/m_W^2),\qquad a\ne b.
$$
If all internal <masses> were equal, $F$ would be common and $\sum_iV_{ai}V_{bi}^*=0$. Subtracting an arbitrary common value makes the suppression explicit:
$$
\boxed{\mathcal A_{a\to b}\propto\sum_iV_{ai}V_{bi}^*\left[F(m_i^2/m_W^2)-F(m_{\mathrm{ref}}^2/m_W^2)\right].}
$$
This is the <Glashow-Iliopoulos-Maiani mechanism>. Unequal <masses> leave small loop-level <Flavor-changing neutral currents>[flavour-changing neutral currents], so the statement that they are never observed would be too strong: the mechanism suppresses them and forbids them at tree level. The cancellation requires complex <CKM> products; the rounded table of absolute values alone must not be summed as if every <phase> were positive.
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