This puts 1/3 the entire weight of the entire stack above directly onto that edge, where the horizontal plywood floor meets the vertical riser. (1/3, because 1/3 is on the center vertical riser, and one third is on the opposite side vertical riser.)
This reduces the entire problem to a simple sheer strength equation. 1/3 of the entire weight of the stack above that point, against that plywood, in sheer.
Would it hold, or would it fail?
We need to know the exact weight of the gold above, and the sheer strength of the plywood.
I think that data should be right in a civil engineering text book, if we can make assumptions about the horizontal wood's compression, tensile and sheer strength.
1/3 of the entire weight is two tons ...
Those tops and bottoms are NOT plywood. take a good look ... they're 6 one-by-four(?) natural boards. Each board is taking 1/6 of two tons or 333 pounds ... approximately the weight of one Michael Moore.
I think it would hold.
"We need to know the exact weight of the gold above"
You can't w/o seeing all the actual bars. How many of them are there? That is the missing term.
Span Elasticity.
Looks like the joists members are 12 inches apart and the pallet is more or less square, that makes the load area 4 square foot. We can plug in some numbers (from a hazy memory) in lieu of more information to check if this is reasonable.
1" APA rated plywood on 12" centers:
Select grade - 1200 psf - 4800 lbs.
Marine grade - 1500 psf - 6000 lbs.
Looks reasonable to me ...