Lumens per square foot?

Hey all, long time outdoor grower getting ready to set up my first indoor grow. I plan to get a 400or 600 wt tent setup butI am a bit confused about the whole lumen per square foot thing. According to what I read

Minimum amount of lighting needed is around 2000 lumens per square foot.
Mid range is around 5000 lumens per square foot.
Optimal is 7000-7500, or higher, lumens per square foot.

Say your space is 3 feet deep by 4 feet wide, 12 square feet. The total lumens available from your light(s) is 45000 lumens. 45000/12 = 3750 lumens per square foot. So say I put a 600 wat, 90,000 lumen HPS in a 5x5 tent thats only 3600 lumens per square foot? SO are these tents a scam bc the numbers dont seem to add up and I dont see me fitting a 600w light in a much smaller tent. I want to make my first indoor grow right, not looking to screw around lol.

the sun puts out 50ooo Lums per sq meter (on an avg clear day)
1 sq meter = 10.76 sq feet = 4646 Lums per sq foot
you can veg w less but to flower you need to hit at least 30ooo Lums sq meter (2788 sq foot)
you can go more than 50ooo L sq M, but i read approaching 90ooo L sq M is damaging/fatal to MJ

12 sq feet = 1.1148 sq meters x 50ooo = 55,740 Lums
x 30ooo = 33,444 Lums

so to equal the sun in your grow-area you need 33-55ooo Lums ...keep in mind the bulb lum rating is taken like 12" or less from the bulb, a reading 2' from the bulb will read much less lums, but a 400w hood set to raise n lower would be fine in there

(my head hurts now, i need a beer)