= Solution
If the driver can be fully depleted with <transformer ratio> six, the largest ideal witness gain from a $62.5$ GeV <proton> is $375$ GeV. Each lepton then has
$$
E_{e,\max}=62.5+6(62.5)=437.5\,\mathrm{GeV}.
$$
For equal opposing <electron> and <Positron> beam energies,
$$
\boxed{E_{\rm CM,max}=875\,\mathrm{GeV}.}
$$
The associated ideal population ratio would be $N_p/N_e=6$. This energy-budget ceiling ignores wake-generation and transfer losses, staging limits, emittance preservation and the difficulty of accelerating both charge signs with suitable focusing. It is the consequence of the stipulated transformer-ratio bound, not a prediction of an achievable upgrade.
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