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In real life, even if the change in geological times is extremely fast, there are many generations of coccoliths within a year (2.8 generations per day during Ehux blooms, or let’s say 300 per year, including winter) or some 3000 generations of Ehux, before CO2 in air doubles (if that is ever reached).
And coccoliths use bicarbonate (not carbonate to make their shells (see the biogeochemistry page of Ehux.