= Solution
The observed dominance of <kaons> supports a predominantly $s\bar s$ <phi meson>. In a connected strong decay, the original strange <quark> and <antiquark> survive into different <kaons>, while a <gluon> produces a light $q\bar q$ pair:
$$
s\bar s\longrightarrow(s\bar q)(q\bar s),\qquad q=u,d.
$$
This gives $K^-K^+$ or $\bar K^0K^0$ and is allowed by the <OZI rule>. A pionic final state contains no strange valence constituents, so the initial $s\bar s$ pair must annihilate. The strong annihilation of a colour-singlet $1^{--}$ state requires at least three <gluons>: one <gluon> cannot carry the <singlet representation>[singlet] colour, and two have the wrong charge-conjugation quantum number. This disconnected <quark flavor>[flavour] topology is suppressed by the <OZI rule>, although it need not vanish.
\Image[/past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2019-phi-decay-topologies.png]
{title=Original quark-level topologies for connected kaon production, three-gluon annihilation into pions, and electromagnetic annihilation into leptons. The hadronization blob is schematic.}
The leptonic mode proceeds through $s\bar s\to\gamma^*\to\ell^+\ell^-$ and is suppressed by <electromagnetic interaction>[electromagnetic couplings]; its width is proportional to $\alpha^2$ times the vector-meson overlap. Unlike a strong <hadron>[hadronic] decay, it cannot create its final <particles> through <quark> rearrangement. Hence a <branching fraction> of order $10^{-4}$ is qualitatively consistent with <electromagnetism>[electromagnetic] annihilation competing with strong modes.
Kaon dominance is especially suggestive because <phase space> is limited: using the supplied neutral-kaon and phi <masses>,
$$
\boxed{p_K=\sqrt{\frac{m_\phi^2}{4}-m_{K^0}^2}\simeq110\ \mathrm{MeV},\qquad
m_\phi-2m_{K^0}=24\ \mathrm{MeV}.}
$$
The two spin-zero <kaons> have <orbital angular momentum> $L=1$ to match the vector parent, so their <partial decay width>[partial width] has the additional near-threshold factor $p_K^3$. Pionic modes have more <phase space> yet remain subdominant because of their annihilation topology. The observations therefore support, but do not establish exact, <ideal vector-meson mixing>: a small nonstrange admixture, <electromagnetism>[electromagnetic] amplitudes and nonperturbative strong dynamics can all contribute to the pionic rate.
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