Unicycle's ultimate speed involves support over beam (8)

I believe the answer is:

eradiate

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'unicycle's ultimate speed involves support' is the definition.
I can't tell whether this defines the answer.

'over beam' is the wordplay.
'over' becomes 'e' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'beam' becomes 'radiate' ('radiate' can be a synonym of 'beam').
'e'+'radiate'='ERADIATE'

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I've seen this clue in The Guardian.

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