It doesn't.
But it seemed a perfectly adequate answer to the question you posed:
"What interest or capacity does the UK have in projecting power in the Pacific independent of the US, is the big question."
It's an interesting hypothesis, but it does not adequately demonstrate that there is anything remotely similar in the congruence of interests, aims and expectations between NA and Europe vis-a-vis the same calculation made for CANZUK countries.
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