The formula
Go Public unlocks once you have earned $5.00Qa (five quadrillion) in the current run. It then pays round(2 × √(run earnings ÷ $5Qa)) Golden Parachutes, never fewer than one — so the first eligible Go Public (at $5.00Qa) already pays 2, $7.81Qa pays 3, $15.31Qa pays 4, $25.31Qa pays 5 and $37.81Qa pays 6. An armed Priority Contract doubles the payout. Each parachute you have ever earned adds +10% to all income, permanently; spending parachutes on backdrop themes does not lower that multiplier.
Why the square root matters
Because the payout grows with the square root of earnings, a run that earns four times as much only pays twice the parachutes. That is why the prestige guide recommends going public when the goal line starts speaking in hours rather than pushing one run forever.
What you keep
Going public resets cash, stations and upgrades, but your lifetime stats, achievements, boost inventory, unlocked backdrops, settings and — since v1.0.3 — your hired managers carry over, and the parachute multiplier applies from the first carton of the next run.