If you charge the cap to 6V, run a low drop-out 4.3V linear regulator and connect the output to your 1 ohm load, you can only maintain the 4.3A as long as the cap voltage is above the input voltage for the linear regulator. It is realistic to get a linear regulator that will produce 4.3A at an overhead of 500mV. This means the end voltage in the above equation goes to 4.8V:
Cap = 4.3 * 20,000/(6-4.8) = 71,667uF
While doable, that is not exactly a small setup. If you were to use 6.3V caps (way too close for my comfort level), you can get 15,000uF caps in 0.75" x 1.5" package. You will need 5 of those in parallel.
If you wanted a safety margin, I would use 6 of 15,000uF, 10V caps (0.75" x 1.75" size) in parallel, feeding a MIC29502 set to operate at 4.3V. The MIC29502's enable input will enable/disable the output current.
---55p
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