I was just astounded anyone would advertise 4000 amps. Then on top of that say there are electronics between the battery and clamps that protects everything. 0.003 ohms at 12.6v is 4000 amps: three milliohms. Two feet of #2 copper takes care of that. Since the batteries being used have somewhere around 6 to 17 mOhm internal resistance ...
The 'truth' the ad does tell is the 22,500 joules over three seconds. That equates to about 600 amps, a bit more amps if you include the battery series resistance and 9.6v test voltage. Though this J3S is not an industry standard specification as far as I know.
FYI, one engineering test of several 100Ah lead acid batteries (Gel, AGM, and flooded) showed a range of dead short currents between 2250 and 5500 amps. And that was a well designed crowbar test, see page 7-4.
--
https://www.sbsbattery.com/PDFs/VRLAshortCurrentsStorageBatterySystems.pdf
I'm a retired test engineering type, so I tend to go overboard on these sorts of electrical measurement things.