is that to many plants?

[daihashi]

Four plants in four square feet is going to be tight. 5 or 6 sq. ft. is more like it for 4 plants. Are you doing a scrog? If not, you'll want to go to flower early.

As for the light...
3000 lumens/sq. ft. = marginal grow
4000 lumens/sq. ft = pretty good grow
5000+ lumens sq. ft. = very good grow

15000 lumens in 4 sq. ft. is going to be pretty marginal. I'd try to get more light.

4 plants in square 3 gallon pots will fit perfectly in a 2'x2' area with a little bit of room to spare.

The rest of your post is correct, however being 5000 lumens off doesn't mean that his grow won't succeed. He can definitely do a grow with 15k lumens in a 4 sqft area.