Air is the means; oxygen is the purpose. DMR asks for oxygen above 10 per cent by volume during Phase II conditioning so the mass stays fully aerobic, and notes demand can climb above 15 per cent of the total gaseous volume during post pasteurisation conditioning.
When oxygen falls the process does not simply slow, it changes. Anaerobic pockets make sour smelling compounds and kill the thermophilic flora. DMR links olive green mould directly to lack of aeration during compost preparation, especially during Phase II, alongside temperatures above 60 degrees.