Additional info:
-If GIB has a balanced 26-27 here, he'll have 5 hearts, as such hands without a 5 card major open 3NT.
-With 3 card support and a balanced hand, he'll use blackwood instead of 6NT.
-If GIB has a 26-29 point hand and a good side suit as well as 3 card support, he'd bid it and then bid 6♠ over your 3♠ rebid, even if blackwood is a better idea.
-If GIB has a 26-29 point hand with a good side suit and 2 card support, he'll bid 6NT over 2♠.
-GIB might bid 6NT with a void spade and 26-29 HCP.
Your call.
Bonus: GIB opened 3NT on another hand with ♠Kx ♥AKx ♦AKQJ9 ♣KQx, I bid 4♠ which is undefined, and GIB bid 5♦ which literally gives no information that wasn't given with the 3NT opener (2-5 diamonds, etc)

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