How to give an evidence in support of the arenium ion mechanism?
You say you've already drawn the energy profile diagram for your proposed mechanism , now you want to make sure that your reaction mechanism proceeds through the most stable transition state , ( Least activation energy ) and therefore , on the energy profile diagram , the peak occuring at the transition state should not be too high .Also you wanna make sure that your final products have energies lesser than the  reactants , because in that case , your $\Delta H$ would be $-ve$ and from the equation $\Delta G=\Delta H-T\Delta S $, there would be a greater chance your reaction moves forward.

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