[Retros] Symmetry - Balanced?

[mr.mip]

I would like to propose following, perhaps more restricted, definition for
'symmetry':

- Let us consider that initially the board with pieces is supported only by
a very thin rod on the centerpoint of the board. We agree that the board is
now balanced (ie. King and Queen have the same 'weight').

-Now after each move pair by white and black this balance is tested.
- If the position retains the balance, then it is called 'symmetric' or
perhaps better 'balanced'.

The presence of equal 'weight' of K and Q will keep the play more
interesting.

Question: What is the shortest mate (If any) in this 'balanced chess'?

Below is one possibility - mate after 6 full moves by black (No surprise
there!)- but you may well do better.

mr.mip

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Here it comes....
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1.f3 c6 2.Kf2 Qc7 3.Ke3 Qd6 4.b3 g6 5.Ba3 Bh6+ 6.Ke4 Qd5#