I agree (more or less, with only minor quibbles) with jdonn (no, it was not a term of our settlement of our recend dispute that we agree with each other

) as to when I would not make a support double. I also agree with Frances as to the idea that 2
♠ should not promise
♣... you have to have an unambiguous game force here, and the cue bid is the logical tool. Restricting it to promised or suggested
♣ support is too narrow a use.
As for the continuation, I am not surprised that there is a difference of opinion: it is an extremely unusual auction: what is LHO doing? Most would (I assume) have bid more
♠ on the previous round: this slow approach is begging to get doubled (when double is right) while an immediate jump would have decreased the bidding space significantly.
As for me, I now reluctantly disagree with Frances as to the meaning of 4
♥: I now take it as 3 card support: a weak hand with good long
♣ checking back for a
♥ suit that could play opposite, say, Jx Qxx Ax KQ109xxx.
I suggest this on the basis of the old saying: game before slam. The partnership is committed to game, but I see no reason why North would bid differently with xx AJ10xx Kx AJxx and I'd rather be in 4
♥ than 5
♣.
It may be that my difference with Frances arises from our somewhat different approach to the first question: when would we not make a support double.
BTW, I saw mike777's suggestion that 4
♦ by opener would be keycard in
♣. I really don't like that idea: I have huge difficulty constructing hands for South, consistent with the pass of 3
♠, that could now take charge and place the contract solely on the basis of how many keycards the unlimited partner holds.
And the idea of never being able to cue bid
♦ leaves me bewildered.
But, I confess, I am almost always protesting that too many players use keycard toys far, far too much...
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari